Question

Given: f(x) = 3x + 4 and g(x) =1/4x -3 find: (a) g(f(x)) (b) f(g(-2)) (c) when f(g(x)) = 5

Answer 1

g(f) = 1/4 f - 3

= (3x+4)/4 - 3
= 3/4 x - 2

f(g(-2)) = f(-7/2) = -13/2

f(g) = 3g+4 = 3(x/4-3)+4 = 3/4 x - 5
f(g)=5 means
3/4 x - 5 = 5
3/4 x = 10
x = 40/3