Determine whether the function f(x) = 3x⁴ is even or odd.

Solution:

A function y = f(x) is an

a) Even function of x if f(-x) = f(x)

b) Odd function of x if f(-x) = -f(x)

For every x in the function's domain

The given function f(x) = 3x⁴

Let us replace x by -x and the behaviour of the function will be :

f(-x) = 3(-x)⁴

= 3x⁴

Hence f(-x) = f(x).

Therefore the function f(x) = 3x⁴ is an even function.

If f(x) = 3x³, then

f(-x) = 3(-x)³

= -3x³

= -f(x)

Which implies that f(x) = 3x³ is an odd function

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Determine whether the function f(x) = 3x⁴ is even or odd.

Summary:

The function f(x) = 3x⁴ is an even function.