Question

Considerando as funções f: R ⟶ R,
g: R ⟶ R definidas por f(x) = 2x + 1,
g(x) = x2
– x + 2 e h(x) = 3 – x, determine:
a) f(g(x))
b) g(f(x))
c) g(f(h(x)))

Answer 1

A) f(g(x)) =f(x2-x+2)=2(x2-x+2)+1
2x4-2x+4+1
2x-2x+4+4+1

f(g(x))=9

B) g(f(x))= (2x+1)2-(2x+1)+2
4x+2-2x-1+2
4x-2x+2-1+2

g(f(x)) 2x+3

C)g(f(h(x)))= (2(3-x)+1)2 -(2(3-x)+1)+2
4(3-4x)+2-(6-2x+1)+2
12-4x+2-6+2x-1+2
-4x+2x+12+2+2-1-6

g(f(h(x)))2x+9