Determine inverse functions

Question

Determine whether f(x) = −2x + 6 and g(x) = −12x + 3 are inverse functions

Answer 1

the easiest way to find the inverse of a function is to swap the x and y and resolve for y

so y= -2x +6 becomes

x=-2y+6

(x-6)=-2y

y= -(x-6)/2

so -12x+3 is not the inverse

Answer 2

Does f(g(x)) = g(f(x)) = x?

f(g(x)) = -2(-12x + 3) + 6 = 24x - 6 + 6 = 24x

Well, 24x ≠ x, so no.