which statement best describes how to determine whether f(x) = 9 - 4x² is an odd function? determine whether…

which statement best describes how to determine whether f(x) = 9 - 4x² is an odd function? determine whether 9 - 4(-x)² is equivalent to 9 - 4x². determine whether 9 - 4(-x²) is equivalent to 9 + 4x². determine whether 9 - 4(-x)² is equivalent to -(9 - 4x²). determine whether 9 - 4(-x²) is equivalent to -(9 + 4x²).
Answer
Answer:
C. Determine whether $9 - 4(-x)^{2}$ is equivalent to $-(9 - 4x^{2})$.
Explanation:
Step1: Recall odd - function definition
A function $y = f(x)$ is odd if $f(-x)=-f(x)$ for all $x$ in the domain of $f$.
Step2: Find $f(-x)$ for $f(x)=9 - 4x^{2}$
Substitute $-x$ into $f(x)$: $f(-x)=9 - 4(-x)^{2}$.
Step3: Find $-f(x)$ for $f(x)=9 - 4x^{2}$
$-f(x)=-(9 - 4x^{2})$.
Step4: Check odd - function condition
To determine if $f(x)$ is odd, we need to check if $f(-x)=-f(x)$, that is, whether $9 - 4(-x)^{2}$ is equivalent to $-(9 - 4x^{2})$.