Question

Let $f ( x )$ and $g ( x )$ be two real polynomials of degree $2$ and $1$ respectively. If $f(g(x))=8 x^{2}-2 x$, and $g(f(x))=4 x^{2}+6 x+1$, then the value of $f(2)+g(2)$ is________.

Answer 1

$f\left(g(x)=8 x^{2}-2 x\right. $
$g\left(f(x)=4 x^{2}+6 x+1\right.$
So, $ g(x)=2 x-1 \,\,\,g(2)=3 $
$\& f(x)=2 x^{2}+3 x+1 $
$f(2)=8+6+1=15$