# How do you find the compositions given #f(x) = |x - 2#|, #g(x) = sqrtx#?

Every function has an input and an output. Composing two functions means to use the output of the first as the input for the second.

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To find the compositions ( f \circ g ) and ( g \circ f ), where ( f(x) = |x - 2| ) and ( g(x) = \sqrt{x} ), we substitute the expression for one function into the other and evaluate.

For ( f \circ g ), we substitute ( g(x) ) into ( f(x) ):

[ f(g(x)) = |g(x) - 2| ]

[ f(g(x)) = | \sqrt{x} - 2| ]

For ( g \circ f ), we substitute ( f(x) ) into ( g(x) ):

[ g(f(x)) = \sqrt{f(x)} ]

[ g(f(x)) = \sqrt{|x - 2|} ]

So, ( f \circ g = | \sqrt{x} - 2| ) and ( g \circ f = \sqrt{|x - 2|} ).

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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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