Question

Dada as funções f(x)=2x+1 , g(x)= -x+7 , h(x)= 3x/2 , determine : a) f(g(x)). b)g(h(x)). c)f(g(x))=f(h(x)). d)f(g(5)). obrigada,boa tarde (:

Answer 1

a) f(g(x)) = 
f(-x+7) = 2.(-x+7)+1 = -2x+14+1 = -2x+15
g(h(x)) = -3x/2 + 7 = -3x/2 + 14/2 = (-3x+14)/2
f(g(x)) = f(h(x))
f(h(x)) = 2.3x/2 + 1 = 3x+1
-2x+15 = 3x+1
-2x-3x = 1-15
-5x = -14
5x = 14
x = 14/5
f(g(5)) = --> g(5) = -5+7 --> g(5) = 2 --> f(g(5)) = f(2) = 2.2 + 1 = 4 + 1 = 5