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If $\mathrm{f}, \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$ be defined by $\mathrm{f}(\mathrm{x})=2 \mathrm{x}+1$ and $\mathrm{g}(\mathrm{x})=\mathrm{x}^2-2$,
$\forall x \in R$, respectively. Then, find gof.
$\forall x \in R$, respectively. Then, find gof.
Solution:
2865 Upvotes
Verified Answer
Here $f(x)=2 x+1$ and
$$
\begin{aligned}
\mathrm{g}(\mathrm{x}) &=\mathrm{x}^2-2, \forall \mathrm{x} \in \mathrm{R} \\
\mathrm{gof} &=\mathrm{g}\{\mathrm{f}(\mathrm{x})\} \\
&=\mathrm{g}(2 \mathrm{x}+1)=(2 \mathrm{x}+1)^2-2 \\
&=4 \mathrm{x}^2+4 \mathrm{x}-1
\end{aligned}
$$
$$
\begin{aligned}
\mathrm{g}(\mathrm{x}) &=\mathrm{x}^2-2, \forall \mathrm{x} \in \mathrm{R} \\
\mathrm{gof} &=\mathrm{g}\{\mathrm{f}(\mathrm{x})\} \\
&=\mathrm{g}(2 \mathrm{x}+1)=(2 \mathrm{x}+1)^2-2 \\
&=4 \mathrm{x}^2+4 \mathrm{x}-1
\end{aligned}
$$
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