# What is the domain of the composite function #(g@f)(x)#?

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To determine the domain of the composite function ((g \circ f)(x)), we need to consider the domains of the individual functions involved and any restrictions they impose on the input values.

Let's denote (f(x)) as the inner function and (g(x)) as the outer function.

First, we find the domain of (f(x)), considering any restrictions on the input values imposed by this function.

Next, we need to ensure that the output of (f(x)) falls within the domain of (g(x)) so that we can evaluate ((g \circ f)(x)). This means we need to check if the output of (f(x)) is within the domain of (g(x)).

The domain of ((g \circ f)(x)) will be the set of all (x) values for which both (f(x)) and (g(x)) are defined and where the output of (f(x)) lies within the domain of (g(x)).

In summary, to find the domain of ((g \circ f)(x)), we need to:

- Determine the domain of (f(x)).
- Determine the range of (f(x)) within the domain of (g(x)).
- Ensure that the range of (f(x)) within the domain of (g(x)) is also within the domain of (g(x)).
- The resulting set of values will be the domain of the composite function ((g \circ f)(x)).

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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.

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