Question

Determine whether each of the following functions is even, odd, or neither even or odd. (a) f(x) = x^5 + x (b) g(x) = 1 - x^6 (c) h(x) = 2x - x^4

Answer 1

Answer with Step-by-step explanation:

Even function: If f(x)=f(-x)

Then, the function is  an even function.

Odd function: If $f(x)\neq f(-x)$

Then, the function is an odd function.

a.$f(x)=x^5+x$

Replace x by -x

$f(-x)=(-x)^5+(-x)=-x^5-x=-(x^5+x)$

$f(x)\neq f(-x)$

Hence, the function is an odd function.

b.$g(x)=1-x^6$

Replace x by -x

$g(-x)=1-(-x)^6=1-x^6$

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

Hence, g(x) is an even function.

c.$h(x)=2x-x^4$

Replace x by -x

$h(-x)=2(-x)-(-x)^4=-2x-x^4$

$h(x)\neq h(-x)$

Hence, h(x) is an odd function.