Question

HomeworkUse the equation to classify the polynomialfunction. Is it even, odd, or neither? SEE EXAMPLE 215. f(x) = 2x5 + 4x2 16. g(x) = 6x4 + 2x2+

Answer 1

Given function,

$f(x)=2x^5+4x^2$

Thus,

$15.f(-x)=2(-x)^5+4(-x)^2=-2x^{5^{}}+4x^2$

Since,

$f(-x)\ne f(x),\text{ }f(-x)\ne-f(x)$

Thus the function is neither odd nor even.

Again,

$16.g(x)=6x^4+2x^2$

Thus,

$g(-x)=6(-x)^4+2(-x)^2=6x^4+2x^2$

So,

$g(-x)=g(x)$

Thus the function is even.