Question

Considere a funçôes f e g IR EM IR definidas por f(x)=x-1 e g(x)=x ao quadrado+x Determine:

(fof)(x)


(gog)(x)

Answer 1

Resolvendo:

f,g:|R → |R

f(x) = x - 1
g(x) = x² + x

(fof)(x) = f(f(x)) = (x-1) - 1 = x - 2 

(gog)(x) = g(g(x)) = (x² + x)² + x = x^4 + 2x³ + x² + x

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04/05/2017
Sepauto
SSRC
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Answer 2

(fof)(x) =
f( f(x) ) =
f(x - 1) =
(x - 1) - 1 =
x - 2

(gog)(x) =
g( g(x) ) =
g(x² + x) =
(x² + x)² + (x² + x) =
(x⁴ + 2x³ + x²) + (x² + x) =
x⁴ + 2x³ + 2x² + x