Question

Show that f(x) = 3x 4 − 2x 2 + 5 is an even function.

Answer 1

Answer:
Step-by-step explanation:
This f(x) is an even function.
Explanation:
An even function is one where f(−x)=f(x) for all x in the domain.
An odd function is one where f(−x)=−f(x) for all x in the domain.
In the case of f(x)=3x4−x2+2 we find:
f(−x)=3(−x)4−(−x)2+2=3x4−x2+2=f(x)
So f(x) is an even function.
Actually, there is a shortcut with polynomial functions:
If all of the terms have even degree then the function is even.
If all of the terms have odd degree then the function is odd.
Otherwise the function is neither odd nor even.
in our example, 3x4 has degree 4, −x2 has degree 2 and 2 has degree 0. So all of the terms are of even degree and the function is even