Question

$f\left(x\right)=x^2+d$ and $g\left(x\right)=2x^2$, where d is a constant. If $\frac{f\left(g\right(2\left)\right)}{f\left(2\right)}=4$, find the value of $d$.

• A. $16$
• B. 5
• C. 22
• D. 18

Answer 1

The correct option is A $16$

Given, $f\left(x\right)=x^2+d$ and $g\left(x\right)=2x^2$

$g\left(2\right)=2\left(2^2\right)=8$

Hence, $f\left(g\right(2\left)\right)=f\left(8\right)=64+d$
Therefore $\frac{f\left(g\right(2\left)\right)}{f\left(2\right)}=\frac{64+d}{4+d}=4$

Hence, $64+d=16+4d$

$\Rightarrow 48=3d$

$\Rightarrow d=16$