Mathematics High School

Determine whether each function is even, odd, or neither.
f(x) = x²_9

g(x) = |x-3

f(x) = 22-1

g(x) = x + x2

Determine Whether Each Function Is Even, Odd, Or Neither.f(x) = X_9g(x) = |x-3f(x) = 22-1g(x) = X + X2

Answers

Answer 1

Rule for even

[tex]\\ \sf\longmapsto \boxed{\sf f(-x)=f(x),x\in D_f}[/tex]

Rule for odd

[tex]\\ \sf\longmapsto \boxed{\sf f(-x)=-f(x),D_f}[/tex]

Here D_f means domain of function.

#1

[tex]\\ \sf\longmapsto f(x)=\sqrt{x^2}-9[/tex]

Take x=4

[tex]\\ \sf\longmapsto f(4)=\sqrt{4^2}-9=4-9=-5[/tex]

[tex]\\ \sf\longmapsto f(-4)=\sqrt{(-4)^2}=4-9=-5[/tex]

Even function✓

#2

[tex]\\ \sf\longmapsto g(x)=|x-3|[/tex]

Take x=2

[tex]\\ \sf\longmapsto g(2)=|2-3|=|-1|=1[/tex]

[tex]\\ \sf\longmapsto g(-2)=|-2-3|=|-5|=5[/tex]

[tex]\\ \sf\longmapsto -g(2)=-1[/tex]

Odd function✓

#3

[tex]\\ \sf\longmapsto f(x)=\dfrac{x}{x^2-1}[/tex]

Take x=3

[tex]\\ \sf\longmapsto f(3)=\dfrac{3}{3^2-1}=\dfrac{3}{9-1}=\dfrac{3}{8}[/tex]

[tex]\\ \sf\longmapsto f(-3)=\dfrac{-3}{(-3)^2-1}=\dfrac{-3}{8}[/tex]

[tex]\\ \sf\longmapsto -f(3)=\dfrac{-3}{8}[/tex]

Odd function ✓

#4

[tex]\\ \sf\longmapsto g(x)=x+x^2[/tex]

Take x=1

[tex]\\ \sf\longmapsto g(1)=1+(1)^2=2[/tex]

[tex]\\ \sf\longmapsto g(-1)=-1+(-1)^2=0[/tex]

[tex]\\ \sf\longmapsto -g(1)=-2[/tex]

Neither✓

Related Questions

Jessica had 289 dollars to spend on 7 books. After
buying them she had 16 dollars. How much did each book cost?

Answers

Answer:

39

Step-by-step explanation:

289-16= 273

273/7= 39

Hope this helps! :)

Answer:

$39

Step-by-step explanation:

let b = cost of each book

289 - 7b = 16

-7b = -273

b = 39

I need help

(No link please)

Answers

Answer:

the formula for finding the perimeter of a rectangle is P=2L+2W

an example of how to find the perimeter is

Explanation:

For a rectangle, its perimeter is the sum of all for sides.

The rectangle has a perimeter of 54. Find the lengths of the unknown side. That is, find S.

54=20+20+S+S

Simplify

54=40+2S

Solve for S

14=2S

S=7

Step-by-step explanation:

What is the first time after midnight that all the digits on the display of a digital clock are prime numbers?

Answers

2:22 am
Hope this helps.

Hey could you help me out please
I really don’t want to disappoint my father and I have too many assignments so can you help?

Answers

Answer:

Step-by-step explanation:

1.)  [tex]c = \sqrt{a^{2} +b^{2} }[/tex]

a = 10, b = 7, c = x?

10+7= x

[tex]10^{2} + 7^{2} =x^{2}[/tex]

100 + 49 = [tex]x^{2}[/tex]

149 = [tex]x^{2}[/tex]

[tex]\sqrt{149} =[/tex] 12.206...

x = 12.2

2.) x + 19 = 21

[tex]x^{2} + 19^{2} =21^{2}\\21^{2}-19^{2} = x^{2}[/tex]

441 - 361 = [tex]x^{2}[/tex]

80 = [tex]x^{2}[/tex]

[tex]\sqrt{80}[/tex] = 8.94

x = 9

3.) x + 16 = 27

[tex]x^{2} + 16^{2}= 27^{2} \\27^{2} -16^{2} =x^{2}[/tex]

729 - 256 = [tex]x^{2}[/tex]

473 = [tex]x^{2}[/tex]

[tex]\sqrt{473}[/tex] = 21.74

x = 21.7

4.) 12.8 + 5.3 = x

[tex]12.8^{2} + 5.3^{2} =x^{2} \\163.84 + 28.09 = x^{2}\\191.93 = x^{2} \\\sqrt{191.93} = 13.85\\x = 13.9[/tex]

8.) x = 11.48 ft

a = 3.5 ft , b = x=? , c = 12 ft

[tex]3.5^{2} + x^{2} =12^{2} \\12.25 +x^{2} =144\\144-12.25=x^{2} \\131.75 = x^{2} \\\sqrt{131.75} =11.48\\x = 11.48[/tex]

9.) x = 32.078 feet

[tex]14^{2} +x^{2} =35^{2}\\196 + x^{2} =1225\\1029 = x^{2} \\\sqrt{1029} = 32.078 ft\\x = 32.078 ft\\[/tex]

10.) perimeter = 31.96

hope this helped a lot

mark me brainliest :D

What is 1 and 1/4 - 3/8?

Answers

Answer:

7/8

Step-by-step explanation:

1 and 1/4 would equal 5/4. This would be 5/4-3/8, which equals 10/8-3/8=7/8

Answer:

0.875

Step-by-step explanation:

How would you convert 12.5% to a fraction?

Answers

Answer:

12.5% as a fraction is written as 25/2

Step-by-step explanation:

step 1; write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the numbers of zeros vital or require according.

step in this case 12.5 has one number after the decimal number so we place 10 in the denominator and remove the decimal point. this will make it 125/10.

step 2: then , this fraction can be simplified. 125/10=(125÷5)/(10÷5) =25/2

Diana made 143 treats for her visit to the nursing home. There are 37 patients and she wants each person to get the same number of treats. How many more treats will she need to make in order for each patient to receive 4 treats?

Answers

D, she needs to make 5 more treats.

Answer:

D) 5 more treats

Step-by-step explanation:

Number of required treats:

37*4 = 148

Remaining number of treats:

148 - 143 = 5

Correct choice is D

Find the product of 21 and (6.3 · 10-4).

1.323 · 10 2
1.323 · 10 -3
0.1323 · 10 -1
1.323 · 10 -2

Answers

Answer:  1.323x10^-2  

Step-by-step explanation:

21*(6.3x10^-4) = 1.323x10^-2

A contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood. They are: 2,400; 1,750; 1,900; 2,500; 2,250; 2,100 Which of the following represents the numerator in the calculation of variance and standard deviation? (225)2 (â€"425)2 (â€"275)2 (325)2 (75)2 (â€"75)2 = 423,750 (650)2 (â€"150)2 (â€"600)2 (250)2 (150)2 (â€"300)2 = 980,000 (250)2 (â€"400)2 (â€"250)2 (350)2 (100)2 (â€"50)2 = 420,000.

Answers

Answer:

∑[ (250)2 (400)2 (250)2 (350)^2 (100)2 (50)2] = 420,000.

Step-by-step explanation:

You first calculate the mean which is  is 2150.

You then subtract 2150 from the 6 values in turn

The first one = 2400 - 2150 = 250.

Then you square each of the 6 results and add them up - this comes to 420,000.

I need help a I don't know what to do

Answers

Answer:

Look at my solution

If you type 75 words in 3 minutes at what rate do you type?

Answers

You type 25 words per minute.

Equation: y=25x.

Hope this helps!!

what is the calculation for 70 increased by 9%

Answers

Answer: 6.3 Increase the number by 9% of its value.

You can spend at most $24 at the fair. Game tickets cost $2 each and ride tickets cost $4 each. You want to buy at least 3 game tickets and more than 2 ride tickets. Write and graph a system of linear inequalities to represent this situation. How many of each ticket could you buy?

Answers

Your game tickets are $6 total. Your ride tickets would run you about $12.

$2 x 3 = 6

$4 x 3 = 12

how do i do all these problems i don't understand surface area?the paper is named volume and surface area of composite figures plz tell me a easy way im in class

Answers

Answer:

gud luk 4 class

Step-by-step explanation:

volume = all the sides times together

surface area = all side's area plus together

Someone could help me with problem 3-75 (b) please

Answers

Answer:

a. is correct

b. not correct

c. not correct

d. is correct

Step-by-step explanation:

3-75:

a) 3x + 7 = x - 1

Subtract 7 on both sides to get 3x = x - 8, then subtract x from 3x to get 2x = -8, finally divide 2 on both sides to get x = -4. (Answer is yes)

b) -2x - 4 = -4x + 3

Add 4 on both sides to get -2x = -4x + 7, then add 4x to -2x to get 2x = 7, finally divide 2 on both sides to get x = 7/2. (Answer is no)

c) -3x + 5 + 5x - 1 = 0

Add 1 on both sides to get -3x + 5 + 5x = 1, then subtract 5 on both sides to get -3x + 5x = -4, next combine -3x and 5x together to get 2x = -4, finally divide 2 on both sides to get x = -2. (Answer is no)

d) -(x - 1) = 4x - 5 - 3x

Combine 4x and -3x together to get

-(x - 1) = x - 5, then add (x - 1) and (x - 5) together to get 2x - 6, next do 2x - 6 = 0 and solve for x, by adding 6 on both sides to get 2x = 6, and finally dividing 2 on both sides to get x = 3. (Answer is yes)

Explanation:

I did the whole 3-75 section for you, but I didn't really understand 3-76, and my brain was already hurting by the time I got to section 3-77, sorry.

Hope this helps though, I did my best :)

if 14 karat gold necklace weighs 1.8 ounces how many ounces of pure gold does it contain

Answers

Answer:

1.05 ounces

Step-by-step explanation:

Purest gold is 24 karat

So ATQ:

(14/24) X 1.8=1.049 OR SAY 1.05(ROUNDED OFF)

Given that the zeros of a quadratic function are −2 and −5, what is the standard form of the quadratic function? A) f(x) = x2 + 5x + 10 B) f(x) = x2 + 7x + 10 C) f(x) = x2 − 5x + 10 D) f(x) = x2 − 7x + 10

Answers

Step-by-step explanation:

x = -2 and x = -5

x + 2 = 0 and x + 5 = 0

(x + 2)(x + 5) = 0

x² + 5x + 2x + 10 = 0

x² + 7x + 10 = 0

Option → B

My sweatshirt rhat i want to buy is $36 today the price is 30% off what is the price of the sweatshirt today​

Answers

36x0.3=10.8

Your answer 10.8$

whats x
-5x + 2 = 67

Answers

x = -13
subtract 2 from 2 and 67 leaves you with
-5x=65
divided both sides by -5
x = -13

Answer:

x=-13

Step-by-step explanation:

Subtract 22 from both sides.

-5x=67-2

Simplify  67-2 to  65.

-5x=65  

3 Divide both sides by -5.

[tex]x=-\frac{65}{5}[/tex]

​

Simplify [tex]\frac{65}{5}[/tex] to 13.

 

x=−13

Find the perimeter. Simplify your answer.

Answers

Answer:

3s+10s+10s+3s=9+3+3+9

26s=24

s=26+24

s=50 cm

Line c passes through points (4, 8) and (1, 13). Line d is parallel to line c. What is the slope of line d?

Answers

If the lines are truly parallel, then they should have the same slope. So, the slope should be 1.66667 (Rounded: 1.7)

For positive acute angles A and B, it is known that cos A = 4/5 and tan B =5/12 Find the value of cos(A + B) in simplest form.

Answers

Answer:

33/16

Step-by-step explanation:

translate figure:RIGHT 2 DOWN 1
note:only use four point when drawing the translation​

Answers

Answer:

Your answer is in the image linked below.

Step-by-step explanation:

When the shape is moved right 2, down 1, you should have this translation,  hope this helps.

What is Integration ?

Answers

Answer:

Integration is the act of bringing together smaller components into a single system that functions as one. These links usually are established between the components of the process and control layer of each system to promote the free flow of data across systems.

Answer:

Integration is the action or process of integrating.

Step-by-step explanation:

The table below shows a proportional relationship. True or False?​

Answers

Answer:

True

Step-by-step explanation:

The power, P(watts), of a car engine is proportional to the square of its speed, s(m/s).
When s=45 P=2200.
Work out the speed (to 1 DP) when the power is 1890 watts

Answers

The speed of the car is 41.7 m/s when the power is 1890 watts.

What is Proportion?

Proportion is defined as an equation on which two or more ratios are made to be equal to each other.

It is given that the power, P is proportional to square of the Speed,s.

If P ∝ s², then P = k s², for some constant k.

When s = 45 m/s, P = 2200 watts

k = P / s² = 2200 / 45² = 1.086

∴ when P = 1890 watts,

1890 = 1.086 × s²

s² = 1740.331

s = 41.717 ≈ 41.7 m/s

Hence, if power is proportional to the square of the speed, then, the speed of the car engine is 41.7 m/s if the power is 1890 watts.

To learn more about Proportion, click:

https://brainly.com/question/11240259

#SPJ1

Help Me WHAT is 2 + 2

Answers

Answer:

4

Step-by-step explanation:

Answer:

= 4

2 + 2 = 4

Step-by-step explanation:

yw :-)

What is -12 3/4 + -5 1/2? Write your answer as a mixed number in simplest terms. ​

Answers

-18 1/4
Have a good day! :)

7/10=r-(-8/9) please help

Answers

Answer:  -(3/10)

Step-by-step explanation:

7/10=r-(-8/9)

(7/10)=r+(8/9)

(7/10)-(8/9)=r

  r =(7/10)-(8/9)

  r =(7/10)*(9/9)-(8/9)*(10/10)    [Multiply each fraction by another fraction equal to one, but with values that will convert the denominator into the same value]

  r =(63/90)-(80/90)

 r = -(27/90)  or -(3/10)

The Smiths spend 6% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $2,880 on entertainment. What was their total budget last year?

Answers

Answer:

Total budget this year = $ 2000 more than last year. Let x = Budget for this year. Money on entertainment = 0.06x = 2760. ⇒ Budget for this ...

Step-by-step explanation:

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