Question:
Mark (√) against the correct answer in the following:
If $f(x)=\left(x^{2}-1\right)$ and $g(x)=(2 x+3)$ then $(g \circ f)(x)=?$
A. $\left(2 x^{2}+3\right)$
B. $\left(3 x^{2}+2\right)$
C. $\left(2 x^{2}+1\right)$
D. None of these
Solution:
$f(x)=\left(x^{2}-1\right)$
$g(x)=(2 x+3)$
$\therefore(g \circ f)(x)=g(f(x))$
$\Rightarrow \mathrm{g}(\mathrm{f}(\mathrm{x}))=2 \mathrm{f}(\mathrm{x})+3$
$\Rightarrow g(f(x))=2\left(\left(x^{2}-1\right)\right)+3=2 x^{2}-2+3=2 x^{2}+1$