# How do you find (f of g of h) if #f(x)=x^2+1# #g(x)=2x# and #h(x)=x-1#?

To find ( (f \circ g \circ h)(x) ) where ( f(x) = x^2 + 1 ), ( g(x) = 2x ), and ( h(x) = x - 1 ), you need to perform the composition in the following order: ( f(g(h(x))) ).

- First, find ( h(x) ) applied to ( x ): ( h(x) = x - 1 ).
- Then, find ( g(x) ) applied to the result of step 1: ( g(h(x)) = g(x - 1) = 2(x - 1) = 2x - 2 ).
- Finally, find ( f(x) ) applied to the result of step 2: ( f(g(h(x))) = f(2x - 2) = (2x - 2)^2 + 1 = 4x^2 - 8x + 5 ).

So, ( (f \circ g \circ h)(x) = 4x^2 - 8x + 5 ).

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Given:

One way of thinking about these function compositions is to go back and forth between the symbols and verbal descriptions of what the functions do.

In our example:

Double

Square

So in symbols we might describe this process thus:

So:

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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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