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Question: If two functions are defined by f(x) = x2 - 3 and g(x) = 1x - 9, then write the domain of the composite function (fog)(x).


A ) R - {9}
B ) (-1, ∞)
C ) (0, ∞)
D ) R

Steps to derive

1 f(x) = x2 - 3 and g(x) = 1x - 9

2 (fog)(x) = f(g(x))
 [Use the definition of composite function.]

3 = f(1x - 9) = 1(x - 9)2 - 3
 [Use g(x) = 1x - 9, f(x) = x2 - 3.]

4 The function (fog)(x) is defined ∀ x ∈ R except at x = 9. Hence, the domain of the composite function is R - {9}.



Hence the right answer is Option A

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