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Iestion $7$ of $11$ , Step $1$ of $1$ $\newline$ Correct $\newline$ Find a formula for the inverse of the following function, if possible. $\newline$ $A(x)=\frac{1}{x-1}$ $\newline$ Answer $\newline$ 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

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Full solution

Q. Iestion

7

of

11

, Step

1

of

1

\newline

Correct

\newline

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

\newline

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

\newline

Answer

\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 function, we start by replacing $A(x)$ with $y$ for convenience. $\newline$ $y = \frac{1}{(x-1)}$
Swap $x$ and $y$ : Next, we swap $x$ and $y$ to find the inverse function. $x = \frac{1}{y-1}$
Solve for $y$ : Now, we solve for $y$ . Multiply both sides by $(y-1)$ to get rid of the fraction. $x(y-1) = 1$
Distribute $x$ : Distribute $x$ on the left side. $xy - x = 1$
Isolate $y$ term: Add $x$ to both sides to isolate the term with $y$ on one side. $\newline$ $xy = x + 1$
Divide by x: Finally, divide both sides by $x$ to solve for $y$ . $y = \frac{x + 1}{x}$

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\newline

1

\newline

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\newline

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