Question

Determine whether the function f (x) = x − x1 is odd, even or neither.

Answer 1

A function is even if $f(x) = f(-x)$;

and if $f(-x) = -f(x)$, then the function is odd;

if $f(-x) \neq f(x) , f(-x)$, then the function is neither

$f(x) = x-x_1\\ f(-x) = -x -x_1 = -(x+x_1)$

Since the function is neither even $(x-x_1)$ or odd $-(x-x_1)$, then it is neither$.$