Question

problem 8: $f(x) = sqrt3{x}$
explanation:
step 1: find $f(-x)$
substitute $-x$ into the function:
$f(-x) = sqrt3{-x}$
simplify (since $sqrt3{-a} = -sqrt3{a}$): $-sqrt3{x}$

Explanation:

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

Substitute \( -x \) into the function \( f(x)=\sqrt[3]{x} \):
\( f(-x) = \sqrt[3]{-x} \)

Step2: Simplify \( f(-x) \)

Using the property of cube roots \( \sqrt[3]{-a}=-\sqrt[3]{a} \), we simplify:
\( f(-x) = -\sqrt[3]{x} \)

Step3: Compare with \( -f(x) \)

We know \( -f(x) = -\sqrt[3]{x} \). Since \( f(-x)=-\sqrt[3]{x}=-f(x) \), the function satisfies the definition of an odd function.

Answer:

Odd