Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = 3x² - 1

Solution:

Given f(x) = 3x² - 1 --- [a]

A function is even if f(x) = f(-x) for all x. This means that the function is the same for +ve x-axis and -ve x-axis, or graphically, symmetric about the y-axis.

A function is odd if f(-x) = -f(x), for all x . That is, the function on one side of x-axis is sign inverted with respect to the other side or graphically, symmetric about the origin

Take f(-x) = 3(-x)² -1

= 3(-1)2(x)² -1

= 3(1)(x)² -1

= 3x² - 1 = f(x)

f(-x) = f(x)

Hence, the given function is an even function.

-f(x) = -3x² + 1. Thus the given function is not an odd function.

Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = 3x² - 1

Summary:

Algebraically the function f(x) = 3x² - 1 is an even function.