Home > CCA2 > Chapter 9 > Lesson 9.1.1 > Problem9-12

9-12.

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

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

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

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

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

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