Question

Determine the range of the function
`\displaystyle f(x)=a\sqrt[3]{bx-c}+d`.

Answer 1

Hi there!

`\large\boxed{(-\infty, \infty)}}`

We are given the function:

`f(x) = a\sqrt[3]{bx-c}+d`

This is the transformation form of a cubic root function. Recall these properties of cubic root functions:

Domain: -∞ < x < ∞ (all real numbers)

Range: -∞ < x < ∞ (all real numbers)

Therefore, the range of the given function is all real numbers, or on (-∞, ∞).