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# Let $f,g:R \rightarrow$R be defined by $f(x)=2x+1$ and $g(x)=x^2-2,\forall x \in R,$respectively. Then, find $g\;of(x)$.

$\begin{array}{1 1} 4x^2 -4x -1 \\ 4x^2+4x-1 \\ 4x^2+4x +1 \\ 4x^2-4x+1 \end{array}$

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• $f;g:R \to R$
• Then $gof =g(f(x)) \qquad \forall x \in R$
$f(x)=2x+1$

$g(x)=x^2-2$

$=g(2x+1)$

$=(2x+1)^2-2$

$=4x^2+4x+1-2$

$=4x^2+4x+1$

Hence $gof(x)=4x^2+4x-1$