Mark (√) against the correct answer in the following:

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:

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

$g(x)=(2 x+3)$

$\therefore(g \circ f)(x)=g(f(x))$

$\Rightarrow \mathrm{g}(\mathrm{f}(\mathrm{x}))=2 \mathrm{f}(\mathrm{x})+3$

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

 

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