Question

Determine algebraically whether the function is even, odd, or neither even nor odd. f(x)=2/x^2

Answer 1

An even function can be reflected across the y axis and map onto itself
example: f(x)=x²
an easy test is
if a function is even, then f(-x)=f(x)

an odd function can be reflected about the origin and map onto itself
example: f(x)=x³
a functio is odd if f(-x)=-f(x)


assuming ya meant $f(x)=\frac{2}{x^2}$

test the f(-x)=f(x) thing

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

yep, same

it is even