Question

Find the composition function $(f\circ g)\left(x\right)$ and its domain.
$f\left(x\right)=x+1,g\left(x\right)=3x$

Answer 1

Since $f\left(x\right)=x+1$ and $g\left(x\right)=3x$

So, $\left(fog\right)\left(x\right)=f\left(g\right(x\left)\right)$

$⟹\left(fog\right)\left(x\right)=f\left(3x\right)=3x+1$

Also, domain of a function are the values which you can put into a function so that you get a viable answer (the answer isn't infinity or a square root of a negative number etc.)

In this function, you can put any value of $x$ from real numbers

Therefore, the domain of the function is set of all real numbers.