Question

the function f is defined as follows. f(x)=\sqrt3{x}+4. find f(-125) and f(216). f(-125)= f(216)=

Explanation:

Step1: Substitute -125 into the function

Substitute \(x = - 125\) into \(f(x)=\sqrt[3]{x}+4\). We know that \(\sqrt[3]{-125}=-5\) since \((-5)\times(-5)\times(-5)=-125\). Then \(f(-125)=\sqrt[3]{-125}+4=-5 + 4\).

Step2: Calculate \(f(-125)\)

\(f(-125)=-5 + 4=-1\).

Step3: Substitute 216 into the function

Substitute \(x = 216\) into \(f(x)=\sqrt[3]{x}+4\). We know that \(\sqrt[3]{216}=6\) since \(6\times6\times6 = 216\). Then \(f(216)=\sqrt[3]{216}+4=6 + 4\).

Step4: Calculate \(f(216)\)

\(f(216)=6 + 4 = 10\).

Answer:

\(f(-125)=-1\)
\(f(216)=10\)