Question

Determine whether the function f, of, x, equals, x, squared, plus, x, to the power 4 , plus, 2f(x)=x
2
+x
4
+2 is even, odd or neither.
Answer
Attempt 1 out of 2
Multiple Choice Answers
odd
neither
even

Answer 1

To determine whether the function \( f(x) = x^2 + x^4 + 2 \) is even, odd, or neither, we follow these definitions:

- A function is **even** if \( f(-x) = f(x) \) for all \( x \).
- A function is **odd** if \( f(-x) = -f(x) \) for all \( x \).

Let's calculate \( f(-x) \):

\[
f(-x) = (-x)^2 + (-x)^4 + 2
\]

Calculating each term:

\[
(-x)^2 = x^2
\]
\[
(-x)^4 = x^4
\]

Putting it together, we get:

\[
f(-x) = x^2 + x^4 + 2
\]

Now, compare \( f(-x) \) with \( f(x) \):

\[
f(x) = x^2 + x^4 + 2
\]

Since \( f(-x) = f(x) \), the function satisfies the condition for being even.

Thus, the answer is:

**even**