Composite inverse function solving

Question

Use the functions
f(x) = x + 5 and  g(x) = 4x − 6 to find the function.

(f ∘ g)−1

Answer 1

(f(g)) = 4x - 6 + 5 = 4x - 1

 

x = 4y - 1

4y = x + 1

y = (1/4)x + 1/4

f(g(x))^-1 = (1/4)x + 1/4

 

Let's check.

 

f(g(f(g(x))^-1)) = 4((1/4)x + 1/4) + 6 - 5 = x + 1 - 1 = x

 

Check.