Question

determine if the following function is even, odd, or neither.
$f(x) = x^2 + 2$
select one:
○ a. odd
○ b. neither
○ c. even

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 \( f(-x) \)

Given \( f(x)=x^{2}+2 \), substitute \( -x \) for \( x \):
\( f(-x)=(-x)^{2}+2 \)
Since \( (-x)^{2}=x^{2} \) (because squaring a negative number gives a positive result), we have \( f(-x)=x^{2}+2 \).

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

We see that \( f(-x)=x^{2}+2 = f(x) \).

Answer:

c. Even