Question

12. Determine if the functions are even, odd, or neither. Show your work to justify your (a) f(x) = x4 + 2x2-1 (b) f(x)+2

Answer 1

A) $f(x)=x^4+2x^2-1$

f(-x) can be obtained by replacing x by -x in the equation for f(x).

If we find out that f(x) = - f(x), then the function is odd.

If f(x) = f(- x), then the function is even.

Here

$f(-x)=(-x)^4+2(-x)^2-1$

$f(-x)=x^4+2x^2-1$

Thus we find out that  $f(-x)=f(x)$.

So the given function is even function.

B) $f(x)=x^{-1} +2$

$f(x)=\frac {1}{x}+2$

We need to get f(- x).

$f(-x)=\frac {1}{-x}+2$

$f(-x)=-\frac {1}{x}+2$

We find out that

$f(-x)\neq f(x) \, and\, also \,f(-x) \neq-f(x)$

Thus the function is neither odd nor nor even.