Question

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

Answer 1

Answer:

The function is even because f(x) = f(−x).

Step-by-step explanation:

we know that

An even function is one for which  

f (−x)=f(x) for all x in its domain.

An odd function is one for which  

f( −x) =−f(x) for all x in its domain

In this problem we have

$f(x)=3x^{4}$

so

$f(-x)=3(-x)^{4}=3x^{4}$

therefore

f (x)=f(-x) for all x in its domain.

Is a even function

Answer 2

Answer:

Option A) The function is even because f(x) = f(−x).

Step-by-step explanation:

We are given the following in the question:

$f(x) = 3x^4$

We have to check whether the given function is odd or even.

Even function:

• $f(-x) = f(x)$

Odd function:

• $f(-x) = -f(x)$

To check, we evaluate f(-x)

$f(x) = 3x^4\\f(-x) = 3(-x)^4 = 3(-1)^4(x)^4 = 3x^4 = f(x)$

Thus, the given function is even.