Question

inverse of functions 5
this is the only question in this section.
question
find $f^{-1}(x)$ if $f(x) = \frac{x + 5}{2}$
answer attempt 1 out of 99
additional solution no solution
$f^{-1}(x) = $

Explanation:

Step1: Replace \( f(x) \) with \( y \)

We start by writing the function as \( y = \frac{x + 5}{2} \). This is a standard first step in finding the inverse of a function, as it helps us work with \( y \) and \( x \) more easily.

Step2: Swap \( x \) and \( y \)

To find the inverse, we swap the roles of \( x \) and \( y \). So we get \( x = \frac{y + 5}{2} \). This is based on the definition of an inverse function, where the input and output of the original function are reversed in the inverse function.

Step3: Solve for \( y \)

First, multiply both sides of the equation \( x = \frac{y + 5}{2} \) by 2 to get rid of the denominator. This gives us \( 2x = y + 5 \). Then, subtract 5 from both sides to solve for \( y \). So \( y = 2x - 5 \).

Step4: Replace \( y \) with \( f^{-1}(x) \)

Now that we have solved for \( y \) in terms of \( x \), we replace \( y \) with \( f^{-1}(x) \) to get the inverse function. So \( f^{-1}(x) = 2x - 5 \).

Answer:

\( f^{-1}(x) = 2x - 5 \)