Question

If the functions $f:R\to R$ and $g:R\to R$ be defined by $f\left(x\right)=2x+1,g\left(x\right)=x^2-2$Find the formulae for $fog$.(2)

Answer 1

The function g o $f:R\to R$ is defined by (g o f)(x) = g (f(x))=g(2x+1) $={(2x+1)}^2-2=4x^2+4x-1$ and f o $g:R\to R$ is defined by (f o g)(x)=f(g(x) $=f(x^2-2)$ $=2(x^2-2)+1=2x^2-3.$