CPM Homework Help : PC Problem 1-37

Find the inverse of each function below. Use correct notation to express your answer. Homework Help ✎
1. f(x) = 3x³ − 5
2. g(x) =
3. h(x) = x² − 2

Step 1(a):

Substitute y for the function notation.

Step 2(a):

Switch every x to y and every y to x.

Step 3(a):

Solve for y.

Step 4(a):

Add 5 to both sides:

Step 5(a):

Divide both sides by 3.

Step 6(a):

Take the cube root of both sides:

y = 3x³ − 5

x = 3y³ − 5

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

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

Answer (a):

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

Hint (b):

Follow the same procedure for (a).

Hint (c):

Follow the same procedure for (a).