Question

is the function $j(x) = 11x^2 - 18$ even, odd, or neither?
even
odd
neither

Explanation:

Step1: Recall the definitions

A function \( f(x) \) is even if \( f(-x)=f(x) \) for all \( x \) in the domain. A function \( f(x) \) is odd if \( f(-x)= -f(x) \) for all \( x \) in the domain.

Step2: Compute \( j(-x) \)

Given \( j(x)=11x^{2}-18 \), substitute \( -x \) for \( x \):
\( j(-x)=11(-x)^{2}-18 \)
Since \( (-x)^{2}=x^{2} \), we have \( j(-x)=11x^{2}-18 \)

Step3: Compare \( j(-x) \) and \( j(x) \)

We see that \( j(-x)=11x^{2}-18 = j(x) \)
So by the definition of an even function, \( j(x) \) is even.

Answer:

A. even