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

Answer 1

Plug g(x) into h(x)

Answer 2

(\[(\sqrt{x-3})^2\]

Answer 3

you'll get x-3

Answer 4

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

Answer 5

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


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

Answer 6

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