Is the function f(x)=x4+3x2

Question

even, odd, or neither? Select the correct answer from the list.(1 point)
The function represented by the equation is

Answer 1

To determine whether the function \( f(x) = x^4 + 3x^2 \) is even, odd, or neither, we can use the definitions of even and odd functions:

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

Let's check \( f(-x) \):

\[ f(-x) = (-x)^4 + 3(-x)^2 \]

Calculating each term:

• \( (-x)^4 = x^4 \)
• \( 3(-x)^2 = 3x^2 \)

Therefore,

\[ f(-x) = x^4 + 3x^2 = f(x) \]

Since \( f(-x) = f(x) \), we conclude that the function \( f(x) = x^4 + 3x^2 \) is even.