Question

question 3
consider the function $g(x) = \sqrt3{x - 4}$
what is the range of this functions inverse?
$\bigcirc\\ (-\infty, \infty)$
$\bigcirc\\ (0, \infty)$
$\bigcirc\\ (-\infty, -4)$
$\bigcirc\\ (-\infty, 0)$

Explanation:

Step1: Recall inverse function property

The range of an inverse function equals the domain of the original function.

Step2: Find domain of $g(x)$

For $g(x)=\sqrt[3]{x-4}$, cube roots accept all real numbers. So the domain of $g(x)$ is all real numbers, written as $(-\infty, \infty)$.

Step3: Match to inverse range

Since the range of $g^{-1}(x)$ is the domain of $g(x)$, the range is $(-\infty, \infty)$.

Answer:

$(-\infty, \infty)$