How do you find the domain of #f(g(x))# when #f(x) = 1/(x+3)# and #g = (-2/x)#?
The domain is
As we have
The arrangement is
Thus,
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The domain of (f(g(x))) is the set of all real numbers except those values of (x) that make the expression undefined.
Find where (g(x)) is undefined. In this case, (g(x) = -2/x), so (g(x)) is undefined when (x = 0).
Next, find where (f(x)) is undefined. (f(x) = 1/(x+3)), so (f(x)) is undefined when (x = -3).
Combine the restrictions from (g(x)) and (f(x)). The domain of (f(g(x))) is all real numbers except (x = 0) and (x = -3).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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