Question

Can somone help me
Let f(x)=2x+2,g(x)=x^2 ,and h(x)=3/x-2. State the domain od the operation.
h(g(x))

Answer 1

\[h(g(x))=h(x^2)=\frac{3}{x^2-2}\]
you may not divide by zero, so set
\[x^2-2=0\] solve for x to get \[x=\pm \sqrt{2}\]
so domain is all real numbers except \[x=\pm \sqrt{2}\]