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If f(x) = (3)/(x-2) and g(x) = sqrt(x + ...

If f(x) = `(3)/(x-2)` and g(x) = `sqrt(x + 1)` , find the domain of `f @ g`.

A

`x ge - 1`

B

`x ne 2`

C

`x ge -1 , x ne 2`

D

`x ge -1 , x ne 3`

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The correct Answer is:
D
The domain of g is `x ge -1` because `x + 1 ge 0` . The domain of `f @ g` consists of all x such that g(x) is in the domain of f . Since g(3) = 2 and 2 is not in the domain of f , 3 must be excluded from the domain of `f @ g` .
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