Given g(x)=√x-3 and h(x)=x^2+5.Find h(g(x))

I already know the solution is x+2, however I need someone to explain to how to arrive at this answer step by step, as I would like to understand how to do this.Thanks

Question

Given g(x)=√x-3 and h(x)=x^2+5.Find h(g(x))

I already know the solution is x+2, however I need someone to explain to how to arrive at this answer step by step, as I would like to understand how to do this.Thanks

anonymous · Answer

Plug g(x) into h(x)

anonymous · Answer

($$(\sqrt{x-3})^2$$

anonymous · Answer

you'll get x-3

anonymous · Answer

then add 5, and you'll have x+2

solomonzelman · Answer

$\normalsize\color{black}{ g(x)=\sqrt{x-3}}$     and      $\normalsize\color{black}{ h(x)=x^2+5}$


$\normalsize\color{black}{ h(x)=x^2+5}$
$\normalsize\color{blue}{ h(g(x))=(\sqrt{x-3}~)^2+5}$
$\normalsize\color{blue}{ h(g(x))=(x-3)+5}$
$\normalsize\color{blue}{ h(g(x))=x-3+5}$
$\normalsize\color{blue}{ h(g(x))=x+2}$

anonymous · Answer

oh ok, now i see what i did wrong. thanks guys!