The following three functions look very similar, but define very different functions. Think about how they are defined and write each as a composition of functions given the information below. (None of the functions in your compositions should be the same as the given function.) 1. sin^4 (x) = f(g(x)) where f(x) = , and g(x) = . 2. sin(sin(x)) = f(g(x)) where f(x) = , and g(x) = . 3. sin x^4 = f(g(x)) where f (x) = , and g(x) = .

The functions are illustrations of composite functions, where multiple functions are combined in one.

(1) sin^4 (x) = f(g(x))

Rewrite the above function as:

So, we have:

From the above equation, we have:

So, we have:

Substitute x for g(x)

Hence, the functions are:   and

2.) sin(sin(x)) = f(g(x))

Rewrite the above function as:

From the above equation, we have:

So, we have:

Substitute x for g(x)

Hence, the functions are:   and

3. sin x^4 = f(g(x))

Rewrite the above function as:

From the above equation, we have:

So, we have:

Substitute x for g(x)

Hence, the functions are:   and

Read more about composite functions at:

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Step-by-step explanation:

Given the following functions :

sin^4 (x) = f(g(x)) where f(x) = and g(x) =

Sin⁴(x) = sin(x)⁴

g(x) = sin(x),

f(x) = f(g(x)) = f(sin(x)⁴) = x⁴

2.) sin(sin(x)) = f(g(x)) where f(x) = , and g(x) =

g(x) = sin(x) ; sinx = x

g(x) = sin(x)

f(x) = f(g(x)) = sin(x) ; sin(x) = x

f(x) = f(g(x)) = f(sin(x))

f(x) = sin(x)

3. sin x^4 = f(g(x)) where f (x) = , and g(x) = .

Here,

g(x) = x⁴

f(x) = f(g(x)) = sin(g(x)) = sin x

f(x) = sinx