Question

What are the domain and range of the function?
f(x) = ^3 square x - 3

Answer 1

Step-by-step explanation:

$f(x) = \sqrt[3]{x - 3}$

The domain of a function are the values of $x$ that you can plug into the function $f(x)$.

Values inside of a root must be non-negative, which means that $x - 3$ must be greater than or equal to zero. We can set up an equation to find the domain:

$x - 3 \geq 0$

$x \geq 3$

With this, we know the domain of the function is $[3, \inf)$.

The range of a function are the values that $f(x)$ can have. Since the equation is a cube root, the value will always be non-negative, meaning the range of the function is $[0, \inf)$.