Question

For the function f defined by f(x)=5x−12 find f(−x),−f(x), and −f(−x).

Answer 1

$f(x) = 5x-12$

$f(-x) = 5(-x)-12 = -5x-12$

$-f(x) = -(5x-12) = -5x+12$

$-f(-x) = -(5(-x)-12) = -(-5x-12) = 5x+12$

This is probably asking you to consider the symmetry of f(x). If f(x) is equal to f(-x), then f is symmetric about the origin. If f(x) is equal to -f(x), then f is symmetric about the y-axis.