CPM Homework Help : CCA2 Problem 9-12

Verify algebraically that $g(x) =\frac { 5 x - 2 } { 3 }$ is the inverse function of $f(x) =\frac { 3 x + 2 } { 5 }$ .

Step 1:

Substitute $f(x)$ into $g(x)$ . Simplify.

$g(f(x))=\frac{5\left(\frac{3x+2}{5}\right)-2}{3}=x$

Step 2:

Substitute $g(x)$ into $f(x)$ . Simplify.

$f(g(x))=\frac{3\left(\frac{5x-2}{3}\right)+2}{5}=x$$

Answer:

Since $f(g(x)) = g(f(x)) = x$ , they are inverse functions.