Question

(a) find the inverse function of $f(x)=8x - 7$.
$f^{-1}(x)=

(b) the graphs of $f$ and $f^{-1}$ are symmetric with respect to the line defined by $y =

question help: video

Explanation:

Step1: Set $y = f(x)$

$y = 8x - 7$

Step2: Solve for $x$ in terms of $y$

$y+7 = 8x$, so $x=\frac{y + 7}{8}$

Step3: Replace $x$ with $f^{-1}(x)$ and $y$ with $x$

$f^{-1}(x)=\frac{x + 7}{8}$

Step4: Recall the symmetry property of inverse - functions

The graphs of a function $y = f(x)$ and its inverse $y = f^{-1}(x)$ are symmetric with respect to the line $y=x$

Answer:

(a) $f^{-1}(x)=\frac{x + 7}{8}$
(b) $x$