jude8959 jude8959
  • 11-09-2017
  • Mathematics
contestada

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

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ghanami
ghanami ghanami
  • 11-09-2017
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



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