Checkpoints 2013 Trouble?

[Sanguinne]

I am having difficult with question 46 in checkpoints
here it is

f:R-->R, f(x)=x(x-4) and g:[3/2,5)-->R, g(x)=x+3
If the function h=f+g, then the domain of the inverse function of h is?

[Jeggz]

So let's start by finding out what h(x) is 
When you add x(x-4) + x+3 you get which is what h(x) equals.
Then, you find out the domain of h(x), and because this is a sum of f(x) + g(x) the domain would be the intersection of the domains of these two functions. Hence the intersection between R and would be just .
Then you sketch the h(x) graph for this domain, and find out the range of h(x). The range of h(x) = Domain of the inverse of h(x)
 Hope that helps 

[Sanguinne]

thank you!!