Question

Find the inverse of the function below and write it in the formyequals=f Superscript negative 1 Baseline left parenthesis x right parenthesisf−1(x).​(b) Verify the relationshipsf(f^-1(x)) and f^-1(f(x))=x​f(x)=3x+5(a) f^-1(x)=.....

Answer 1

Answer:

a. $f^{-1}(x)=\frac{x-5}{3}$.

b. See below

Step-by-step explanation:

The given function is: $f(x)=3x+5$

To find the inverse function, we let $y=3x+5$.

We interchange x and y to obtain:  $x=3y+5$.

We now solve for y;

First add -5 to both sides of the equation;

$x-5=3y$.

Divide both sides by 3

$\frac{x-5}{3}=y$.

Or

$y=\frac{x-5}{3}$.

The inverse function is $f^{-1}(x)=\frac{x-5}{3}$.

b.

Let us now verify that;

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

$\implies f^{-1}(f(x))=\frac{3x+5-5}{3}$

$\implies f^{-1}(f(x))=\frac{3x}{3}$

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

$\implies f^{-1}(f(x))=x$

$\boxed{Q.E.D}$