Question

determine whether the function, $f(x) = -4x + 7$, is invertible
○ invertible
○ non-invertible
if so, find the inverse.
$f^{-1}(x) = \square$

Explanation:

Step1: Check if function is one-to-one

A linear function $f(x)=mx+b$ with $m
eq0$ is one-to-one. Here $m=-4
eq0$, so it is invertible.

Step2: Set $y=f(x)$

$y = -4x + 7$

Step3: Solve for $x$

Subtract 7 from both sides: $y - 7 = -4x$
Divide by -4: $x = \frac{y - 7}{-4} = \frac{7 - y}{4}$

Step4: Swap $x$ and $y$ to get inverse

$f^{-1}(x) = \frac{7 - x}{4}$

Answer:

invertible
$f^{-1}(x) = \frac{7 - x}{4}$