For the real-valued functions = g(x)=x^2-3 and h(x) = sqrt(x-6), find the
composition g∘h and specify its domain using interval notation.
Substitute the right side of h(x) for x in the equation for g(x)
Since g∘h = g(h(x)), we cannot substitute anything for x unless it is in the
domain of h, and also what we substitute for x must not cause h(x) to produce
any values which are not in the domain of g.
We find the domain of h:
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-3 -2 -1 0 1 2 3 4 5 6 7 8
which in interval notation is
The domain of g, since g is a polynomial function, is "all real numbers",
which is written
Thus h cannot produce any value which is not in the domain of g, so the
domain of g∘h is the same as the domain of h
Edwin