Question

-inverse functions Find the formula for f^-1(x): F(x) = 3x^3 - 5

Answer 1

Writing the Inverse of a Function

Answer:

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

Step-by-step explanation:

Please refer to my Answer from this Questions to know more about Inverse Functions: brainly.com/question/24619467

Let $y = f(x)$ so that the inverse of $y$ is equal to $f^{-1}(x)$.

Solving for $f^{-1}(x)$:

$f(x) = 3x^3 -5 \\ y = 3x^3 -5 \\ x = 3y^3 -5 \\ 3y^3 -5 = x \\ 3y^3 = x +5 \\ y^3 = \frac{x +5}{3} \\ y = \sqrt[3]{\frac{x +5}{3}}$

Since the inverse of $y$ is equal to $f^{-1}(x)$, $f^{-1}(x) = \sqrt[3]{\frac{x +5}{3}}$.