Dana jest funkcja

$f\left(x\right)=x^2+2$

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a)

$g\left(x\right)=f\left(x+1\right)$  

$f\left(x+1\right)={\left(x+1\right)}^2+2=x^2+2x+1+2=x^2+2x+3$  

Zatem

$g\left(x\right)=x^2+2x+3$  

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b)

$g\left(x\right)=f\left(3-5x\right)$  

$f\left(3-5x\right)={\left(3-5x\right)}^2+2=9-30x+25x^2+2=25x^2-30x+11$  

Zatem

$g\left(x\right)=25x^2-30x+11$  

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c)

$g\left(x\right)=f\left(x^2-1\right)$  

$f\left(x^2-1\right)={\left(x^2-1\right)}^2+2=x^4-2x^2+1+2=x^4-2x^2+3$  

Zatem

$g\left(x\right)=x^4-2x^2+3$