Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

iestion 7 of 11, Step 1 of 1
Correct
nd a formula for the inverse of the following function, if possible.

A(x)=(1)/(x-1)
nswer
How to enter your answer (opens in new window)
Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered an

A^(-1)(x)=
does not have an inverse functi

iestion $7$ of $11$ , Step $1$ of $1$ $\newline$ Correct $\newline$ nd a formula for the inverse of the following function, if possible. $\newline$ $A(x)=\frac{1}{x-1}$ $\newline$ nswer $\newline$ How to enter your answer (opens in new window) $\newline$ Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered an $\newline$ $A^{-1}(x)=$ $\newline$ does not have an inverse functi

View step-by-step help

View step-by-step help

Full solution

Q. iestion

7

of

11

, Step

1

of

1

\newline

Correct

\newline

nd a formula for the inverse of the following function, if possible.

\newline

A(x)=\frac{1}{x-1}

\newline

nswer

\newline

How to enter your answer (opens in new window)

\newline

Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered an

\newline

A^{-1}(x)=

\newline

does not have an inverse functi

Replace with $y$ : To find the inverse of the function $A(x) = \frac{1}{x-1}$ , we need to switch the roles of $x$ and $y$ and then solve for $y$ . Let's start by replacing $A(x)$ with $y$ for clarity. $\newline$ $y = \frac{1}{x-1}$
Switch $x$ and $y$ : Now we switch $x$ and $y$ to find the inverse function. $\newline$ $x = \frac{1}{y-1}$
Eliminate fraction: Next, we solve for $y$ . To do this, we'll first get rid of the fraction by multiplying both sides of the equation by $(y-1)$ . $x(y-1) = 1$
Distribute $x$ : Distribute $x$ on the left side of the equation. $xy - x = 1$
Isolate y: Now, we want to isolate y on one side of the equation. To do this, we'll add x to both sides. $\newline$ $xy = x + 1$
Divide by x: Finally, we divide both sides by $x$ to solve for $y$ . $y = \frac{x + 1}{x}$

More problems from Power rule

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 2 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 1 month ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 1 month ago

Question

\newline

32^{(-1/5)}

Posted 1 month ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 1 month ago