Question 316056
{{{h(x)=1/(sqrt(x)-1)}}} Start with the second function.



{{{h(g(x))=1/(sqrt(1/(x^2))-1)}}} Plug in {{{g(x)=1/(x^2)}}}



{{{h(g(x))=1/(sqrt(1)/sqrt(x^2)-1)}}} Break up the square root.



{{{h(g(x))=1/(1/sqrt(x^2)-1)}}} Take the square root of 1 to get 1.



{{{h(g(x))=1/(1/x-1)}}} Take the square root of {{{x^2}}} to get 'x' (this is assuming that 'x' is non-negative)



{{{h(g(x))=1/(1/x-x/x)}}} Rewrite the second '1' as {{{x/x}}}



{{{h(g(x))=1/((1-x)/x)}}} Combine the lower fractions.



{{{h(g(x))=x/(1-x)}}} Take the reciprocal of the lower fraction.



So the composite function is {{{h(g(x))=x/(1-x)}}}