Question

Dadas as funções f(x) = -x2 + 2 e g(x) = 3x – 5. Calcule:
(a) fog(x) (b) gof(-3) (c) fof(1)

Answer 1

Vamos lá:

→ $f\left(x\right)=-x^2+2$
→ $g\left(x\right)=3x-5$
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a)
$fog\left(x\right)=f\left(g\left(x\right)\right)\\fog\left(x\right)=-\left(3x-5\right)^2+2\\fog\left(x\right)=-\left(9x^2-30x+25\right)+2\\fog\left(x\right)=-9x^2+30x-25+2\\fog\left(x\right)=-9x^2+30x-23$
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b)
$f\left(-3\right)=-\left(-3\right)^2+2\\f\left(-3\right)=-9+2\\f\left(-3\right)=-7\\\\gof\left(-3\right)=g\left(f\left(-3\right)\right)\\gof\left(-3\right)=g\left(-7\right)\\g\left(-7\right)=3\cdot \left(-7\right)-5\\g\left(-7\right)=-21-5\\g\left(-7\right)=-26$
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c)
$f\left(1\right)=-\left(1\right)^2+2\\f\left(1\right)=-1+2\\f\left(1\right)=1\\\\fof\left(1\right)=f\left(f\left(1\right)\right)\\fof\left(1\right)=f\left(1\right)\\fof\left(1\right)=1$
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Espero ter ajudado!