Question

Show that f and g are inverse functions (a) algebraica

(b) graphically, and (c) numerically.
129. f(x) = 3 – 4x, g(x) = 3-x/4

Answer 1

(a) algebraically

(f ° g)(x) = f(g(x))
(f ° g)(x) = f(3 - x/4)
(f ° g)(x) = 3 - 4(3 - x/4)
(f ° g)(x) = x

(g ° f)(x) = g(f(x))
(g ° f)(x) = g(3 - 4x)
(g ° f)(x) = (3 - (3 - 4x))/4
(g ° f)(x) = x

since both ways ended up with “x” as their answers that means they are inverse of each other. i found this doing it algebraically.

i hope this was helpful!