Question 54929
Yes, you did it correctly, but you should finish the problem by replacing y with {{{g^(-1)(x)}}} so you have:
{{{g^(-1)(x) = x^2+4}}}

To check you solution, remember that:
{{{g(g^(-1))(x) = x}}} and {{{g^(-1)(g(x)) = x}}}

Let's look at the first check: {{{g(x) = sqrt(x-4)}}}
{{{g(g^(-1)(x)) = x}}}
{{{g(x^2+4) = sqrt((x^2+4)-4)}}} Simplifying this, you get:
{{{sqrt(x^2) = x}}} This checks out fine.

Now we'll do the second check:
{{{g^(-1)(g(x)) = x}}}
{{{g^(-1)(sqrt(x-4)) = sqrt((x^2+4)-4)}}} Simplifying this, you get:
{{{sqrt(x^2) = x}}} This also checks.