Question

is the function c(x) = 5x⁴ + 3 even, odd, or neither? even odd neither submit

Explanation:

Step1: Recall definitions of even/odd functions

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

Step2: Compute \( c(-x) \) for \( c(x) = 5x^4 + 3 \)

Substitute \( -x \) into \( c(x) \):
\( c(-x) = 5(-x)^4 + 3 \).
Since \( (-x)^4 = x^4 \) (because any even power of a negative number is positive), this simplifies to:
\( c(-x) = 5x^4 + 3 \).

Step3: Compare \( c(-x) \) with \( c(x) \) and \( -c(x) \)

We have \( c(x) = 5x^4 + 3 \), so \( c(-x) = c(x) \).
This matches the definition of an even function (and does not match the definition of an odd function, since \( -c(x) = -5x^4 - 3
eq c(-x) \)).

Answer:

even