Question

Use the algebraic rules for even and odd functions to classify each function as even odd or neither

Answer 1

Explanation:

f(x)=-2x³+x-3

-f(x)=2x³-x+3

f(-x)=-2(-x)³+(-x)-3

=2x³-x-3

it is not equal to f(x) or -f(x)

so it is neither even or odd.

`f(x)=(x+5)/(x) \\f(-x)=(-x+5)/(-x) =(x-5)/(x) \\it ~is~neither~equal~to~f(x)~or~-f(x)\\`

it is neither even or odd.

f(x)=x^4-x^2+10

f(-x)=(-x)^4-(-x)^2+10=x^4-x^2+10=f(x)

it is an even function.

`f(x)=(5)/(-x^2+1) \\f(-x)=(5)/(-(-x)^2+1) =(5)/(-x^2+1) =f(x)\\`

it is an even function.

`f(x)=(-2)/(5x) \\f(-x)=(-2)/(-5x) =(2)/(5x) =-f(x)\\it~ is ~an ~odd ~function.\\`

f(x)=x^9-x^5+4x^3

f(-x)=(-x)^9-(-x)^5+4(-x)^3

=-x^9+x^5-4x^3

=-(x^9-x^5+4x^3)

=-f(x)

it is an odd function.