Question

find the inverse function of the function $f(x) = \frac{1}{3}x + 4$.
answer attempt 1 out of 2
$\circ$ $f^{-1}(x) = 3x - 4$ $\circ$ $f^{-1}(x) = \frac{1}{3}x - 12$
$\circ$ $f^{-1}(x) = 3x - 12$ $\circ$ $f^{-1}(x) = \frac{1}{3}x - 4$

Explanation:

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

$y = \frac{1}{3}x + 4$

Step2: Swap $x$ and $y$

$x = \frac{1}{3}y + 4$

Step3: Isolate the term with $y$

$x - 4 = \frac{1}{3}y$

Step4: Solve for $y$

$y = 3(x - 4) = 3x - 12$

Step5: Replace $y$ with $f^{-1}(x)$

$f^{-1}(x) = 3x - 12$

Answer:

$\boldsymbol{f^{-1}(x) = 3x - 12}$ (the second option in the left column)