Question

inverse of functions challenge
this is the only question in this section.
question
find $f^{-1}(x)$ if $f(x) = \frac{3x - 12}{6}$
answer attempt 1 out of 99
additional solution no solution
$f^{-1}(x) = \square$ submit answer

Explanation:

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

We start by letting \( y = f(x) \), so the function becomes \( y=\frac{3x - 12}{6} \).

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

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x=\frac{3y - 12}{6} \).

Step3: Solve for \( y \)

First, multiply both sides of the equation by 6 to get rid of the denominator: \( 6x=3y - 12 \).
Then, add 12 to both sides: \( 6x + 12=3y \).
Finally, divide both sides by 3: \( y = 2x+4 \).

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

After solving for \( y \), we replace \( y \) with \( f^{-1}(x) \), so \( f^{-1}(x)=2x + 4 \).

Answer:

\( f^{-1}(x)=2x + 4 \)