Question

If f(x) = x + 8 and h(x) = 3x − 3, find a function g such that g ∘ f = h.

Answer 1

hello :
If f(x) = x + 8 and h(x) = 3x − 3,
g ∘ f = h
g ∘ (f ∘ f ^-1) = h ∘ f ^-1 ( proprety associative)
but ;
(f ∘ f ^-1) = x

g ∘ x = g
g(x) = (h ∘ f ^-1)(x)
calculate : (f ^-1)(x)
f(x) = x +8
x= f(x) - 8
so : (f ^-1)(x) = x - 8
g(x) = (h ∘ f ^-1)(x) = h((f ^-1)(x)) = h(x - 8) = 3(x - 8) -3
g(x) = 3x - 27