Question

If $f\left(x\right)=2x^2-1$ and $g\left(x\right)=3x+1$. Find $fog\left(3\right),gof\left(\frac{1}{2}\right)$

Answer 1

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

we know $fog\left(x\right)=f\left(g\right(x\left)\right)$ and $gof\left(x\right)=g\left(f\right(x\left)\right)$

therefore $fog\left(3\right)=f\left(g\right(3\left)\right)$

$g\left(3\right)=3\left(3\right)+1=10,f\left(g\right(3\left)\right)=f\left(10\right)=2\left(100\right)-1=199$

$f\left(1/2\right)=\frac{-1}{2},g\left(f\right(\frac{1}{2}\left)\right)=g\left(\frac{-1}{2}\right)=3\left(\frac{-1}{2}\right)+1=\frac{-1}{2}$