Question

If functions $f,g:R\to R$ are defined as $f\left(x\right)=x^2+1,g\left(x\right)=2x-3$, then find $fog\left(x\right),gof\left(x\right)$ and $gog\left(3\right)$

Answer 1

Given $f\left(x\right)=x^2+1$ and $g\left(x\right)=2x-3$

$fog\left(x\right)=f\left(g\right(x\left)\right)=f(2x-3)={(2x-3)}^2+1=4x^2-12x+9+1=4x^2-12x+10$

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