### Home > PC > Chapter 1 > Lesson 1.1.3 > Problem1-37

1-37.

Find the inverse of each function below. Use correct notation to express your answer.

1. $f\left(x\right) = 3x^{3} − 5$

Substitute y for the function notation.

Switch every $x$ to $y$ and every $y$ to $x$.

Solve for y.

Divide both sides by 3.

Take the cube root of both sides.

$\small \sqrt[3]\frac{x+5}{3}$

$y = 3x^{3} − 5$

$x = 3y^{3} − 5$

$\textit{x} + 5 = 3\textit{y}^{3}$

$\frac{x+5}{3} = \textit{y}^3$

2. $g(x)=\sqrt{2x+4}$

Follow the same procedure for (a).

3. $h(x)=\frac{1}{2}x^2−2$

Follow the same procedure for (a).