Question

10.1 inverses of simple quadratic and cubic functions

Answer 1

The inverse function of the cubic function is its opposite

The inverse function of $f(x) = 5x^3$ is $f^{-1}(x) = \sqrt[3]{\frac x5}$

How to determine the inverse of the function?

The cubic function is given as:

$f(x) = 5x^3$

Express f(x) as y

$y = 5x^3$

Swap the positions of x and y

$x = 5y^3$

Divide both sides by 5

$y^3 = \frac x5$

Take the cube roots of both  sides

$y = \sqrt[3]{\frac x5}$

Express y as an inverse function

$f^{-1}(x) = \sqrt[3]{\frac x5}$

Hence, the inverse function of $f(x) = 5x^3$ is $f^{-1}(x) = \sqrt[3]{\frac x5}$

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