The functions g and h are defined by:

g(x) = In (x+1), x>-1

h(x) = 1/(x+2) + 2, x<-2

i) Explain why the composite function gh cannot be formed.

ii) Find the largest possible domain of h such that gh is a function and state the range of gh.

[Ans. (i) R_{h} ?D_{g} (where ?denotes "is not a subset of") (ii) (-?, -7/3), (-?, In3) ]

after drawing a graph, i figured out the first part of the question. but the second part stumps me.

i know for one thing, for gh to be a function, R_{h} =D_{g} (where = denotes "is a subset of")

with that in mind, i plotted a graph of h without the domain constraint, and checked the range for which y>-1.

but i end up with a range of (2, +?) and thus a domain of (-2, +?)

can anyone help me? thanks.