# How do you determine the three functions f, g, and h such that #(f o g o h)(x) = sin^2(x+1)#?

To determine the functions ( f ), ( g ), and ( h ) such that ((f \circ g \circ h)(x) = \sin^2(x+1)), you need to consider the composition of functions and how they relate to the given expression.

Given that ( \sin^2(x+1) ) is a composite function, we can break it down into simpler components.

- The innermost function ( h(x) ) should produce the argument ( x+1 ) for the sine function.
- The middle function ( g(x) ) should produce ( \sin(x+1) ) from the output of ( h(x) ).
- The outermost function ( f(x) ) should square the output of ( g(x) ), resulting in ( \sin^2(x+1) ).

Therefore, the functions ( f(x) ), ( g(x) ), and ( h(x) ) can be determined as follows:

- Let ( h(x) = x + 1 ).
- Let ( g(x) = \sin(h(x)) = \sin(x + 1) ).
- Let ( f(x) = g(x)^2 = (\sin(x + 1))^2 ).

So, the functions are:

[ h(x) = x + 1 ] [ g(x) = \sin(x + 1) ] [ f(x) = (\sin(x + 1))^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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