Question Find the values of $f(-8)$ and $f(125)$ for the function $f(x) = \sqrt[3]{x} - 3$ .

Studdy Solution

STEP 1

Assumptions
1. The function $f(x)$ is defined as $f(x)=\sqrt[3]{x}-3$ .
2. We need to find the values of $f(-8)$ and $f(125)$ .

STEP 2

To find $f(-8)$ , substitute $x=-8$ into the function $f(x)$ .
$f(-8) = \sqrt[3]{-8} - 3$

STEP 3

Calculate the cube root of $-8$ .
$\sqrt[3]{-8} = -2$

STEP 4

Substitute the cube root of $-8$ back into the function.
$f(-8) = -2 - 3$

STEP 5

Calculate the value of $f(-8)$ .
$f(-8) = -2 - 3 = -5$

STEP 6

To find $f(125)$ , substitute $x=125$ into the function $f(x)$ .
$f(125) = \sqrt[3]{125} - 3$

STEP 7

Calculate the cube root of $125$ .
$\sqrt[3]{125} = 5$

STEP 8

Substitute the cube root of $125$ back into the function.
$f(125) = 5 - 3$

STEP 9

Calculate the value of $f(125)$ .
$f(125) = 5 - 3 = 2$
The solutions are: $\begin{array}{l} f(-8)=-5 \\ f(125)=2 \end{array}$

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