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

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