Question

Let $f\left(x\right)=3x+1$ and $g\left(x\right)=x^2+2$ then find $fog$.

Answer 1

Given, $f\left(x\right)=3x+1$ .....(1) and

$g\left(x\right)=x^2+2$ ......(2).

Now,

$\left(fog\right)\left(x\right)$

$=f\left[g\right(x\left)\right]$

$=f(x^2+2)$ [ Using (2)]

$=3(x^2+2)+1$ [ Using (1)]

$=3x^2+7$.