# Let #f(x)=x^2# and #g(x)=sqrtx#, how do you find the domain and rules of #(f@g)(x)#?

Please see below.

The rule

Thus, we conclude with

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To find the domain and rules of ((f@g)(x)), which represents the composition of functions (f) and (g), first, we need to understand that the composition (f@g) means (f(g(x))).

Given (f(x) = x^2) and (g(x) = \sqrt{x}), we need to find (f(g(x))).

Substitute (g(x)) into (f(x)) to get (f(g(x)) = (g(x))^2).

Thus, ((f@g)(x) = (\sqrt{x})^2).

Simplify ((\sqrt{x})^2) to (x).

Therefore, ((f@g)(x) = x).

The domain of ((f@g)(x)) is the same as the domain of (g(x)), which is (x \geq 0) since the square root function is defined only for non-negative real numbers.

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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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