Question

the function f is defined as follows.
$f(x) = \sqrt3{x - 8}$
find $f(-117)$ and $f(8)$.
$f(-117) = \square$
$f(8) = \square$

Explanation:

Step1: Find \( f(-117) \)

Substitute \( x = -117 \) into \( f(x)=\sqrt[3]{x - 8} \).
\( f(-117)=\sqrt[3]{-117 - 8}=\sqrt[3]{-125} \)
Since \( (-5)^3=-125 \), \( \sqrt[3]{-125}=-5 \).

Step2: Find \( f(8) \)

Substitute \( x = 8 \) into \( f(x)=\sqrt[3]{x - 8} \).
\( f(8)=\sqrt[3]{8 - 8}=\sqrt[3]{0} \)
Since \( 0^3 = 0 \), \( \sqrt[3]{0}=0 \).

Answer:

\( f(-117)=-5 \)
\( f(8)=0 \)