1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
larisa [96]
3 years ago
11

Which of these functions has an inverse function? Select all that apply.

Mathematics
2 answers:
allochka39001 [22]3 years ago
6 0

Answer:

The function x=y and y=x^{3} are inverse function.

Step-by-step explanation:

Function inverse definition:

If a provided function <em>f(x)</em> is mapped <em>x</em> to <em>y</em>, then the inverse of the provided function <em>f(x) </em>is mapped <em>y</em> to <em>x</em>.

Or  f(x)=f(y)\Rightarrow x=y

Now, consider the function <em>y</em> =<em> x</em>.

Interchange the variables <em>x</em> and <em>y</em>.

x=y

Now, solve x=y for y.

x=y

Therefore, this function has an inverse.

Consider the function y=x^{2}.

Interchange the variables <em>x</em> and <em>y</em>.

x=y^{2}

Now, solve x=y^{2} for y.

\pm \sqrt{x} =y

Therefore, the function has no inverse.

Consider the function y=x^{3}.

Interchange the variables <em>x</em> and <em>y</em>.

x=y^{3}

Now, solve x=y^{3} for y.

\sqrt[3]{x}=y

Therefore, the function has inverse.

Consider the function y=x^{4}.

Interchange the variables <em>x</em> and <em>y</em>.

x=y^{4}

Now, solve x=y^{4} for y.

\pm \sqrt[4]{x}=y

Therefore, the function has no inverse.

Hence, the function x=y and y=x^{3} are inverse function.

ElenaW [278]3 years ago
5 0

ANSWER

y=x

y=x³

EXPLANATION

A function, f(x) has an inverse if and only if

f(a) = f(b)   \Rightarrow \: a = b

Thus, the function is one to one.

For y=x or

f(x) = x

f(a) = f(b)   \Rightarrow \: a = b

Hence this function has an inverse.

For the function y=x² or f(x)=x².

f(a) = f(b)   \Rightarrow \:  {a}^{2} =  {b}^{2} \Rightarrow \: a =  \pm \: b

This function has no inverse on the entire real numbers.

For the function y=x³ or f(x)=x³

f(a) = f(b)   \Rightarrow \:  {a}^{3} =  {b}^{3} \Rightarrow \: a = b

This function also has an inverse.

For y=x⁴ or f(x) =x⁴

f(a) = f(b)   \Rightarrow \:  {a}^{4} =  {b}^{4} \Rightarrow \: a =  \pm \: b

This function has no inverse over the entire real numbers.

You might be interested in
What is the solution to the equation 1/4x +2= -5/8x - 5
nalin [4]

Answer:

x = -8

Step-by-step explanation:

1/4x +2= -5/8x - 5

Add 5/8x to each side

1/4x +5/8x +2= -5/8x+5/8x - 5

1/4x+5/8x +2=  - 5

Subtract 2 from each side

1/4x+5/8x +2-2=  - 5-2

1/4x+5/8x =  - 7

Get a common denominator

1/4 *2/2 x + 5/8x = -7

2/8x + 5/8x = -7

7/8x = -7

Multiply each side by 8/7

8/7x * 7/8x = -7 *8/7

x = -8

7 0
3 years ago
Read 2 more answers
Simplify fractions 25 z to 2nd power over 150 z to 3rd power
Darina [25.2K]

Answer:

1/6z.

Step-by-step explanation:

25z^2 / 150z^3

25 divides 6 times into 150 and z^3 / z^2 = z

so the answer is 1/6z.

6 0
2 years ago
1. 1/48 simplified
Hatshy [7]

Answer:

The answer is 10

Step-by-step explanation:

\frac{1}{2} x = 5 \\ x = 10

3 0
2 years ago
1. Gummy worms are $3.50 per pound
Alexxandr [17]
The constant of proportionality is 3.50 since gummy worms are sold at the same rate per pound.

3.50x, equation
3.50(2.5) = $8.75 for 2.5 pounds
3 0
3 years ago
I will you brainiest if you can answer this
Trava [24]
The answer is =3125x
3 0
3 years ago
Other questions:
  • which explains the correct way to move the decimal point to find the quotient in the problem 12.46 divided by 100? My choices ar
    13·1 answer
  • How do I solve <br>-9+8k=7+4k
    13·1 answer
  • Find the surface area of the pyramid shown to the nearest whole number.
    6·1 answer
  • A rhombus is enlarged and has a new perimeter of 40 feet. If the original perimeter was 10 feet, by what factor was the rhombus
    9·2 answers
  • Please answer this correctly
    6·1 answer
  • Independent Practice
    15·1 answer
  • Help me out please??
    11·2 answers
  • Express the ratio 14 inches to 3 feet as a fraction in simplest form
    13·1 answer
  • Me. Perry pays $340 per month to lease her car. How much will she pay to lease her car for two years
    9·2 answers
  • A bus has three passengers Crew Marty Blakely. Marty's age is 1.5 times Crew's age. Blakely's age is 0.75 times crew's age. If t
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!