Question

is the function k(x) = 3x² - 1 even, odd, or neither? even odd neither

Explanation:

Step1: Recall the definitions

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

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

Given \( k(x) = 3x^2 - 1 \), substitute \( -x \) for \( x \):
\( k(-x) = 3(-x)^2 - 1 \)
Since \( (-x)^2 = x^2 \), this simplifies to:
\( k(-x) = 3x^2 - 1 \)

Step3: Compare \( k(-x) \) with \( k(x) \) and \( -k(x) \)

We have \( k(x) = 3x^2 - 1 \), so \( k(-x) = k(x) \). Also, \( -k(x) = - (3x^2 - 1) = -3x^2 + 1 \), which is not equal to \( k(-x) \).

Answer:

even