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Functions of Functions

1. If f(x)=2x-3 and g(x)=x2+1, find each of the following:

a) f(g(2))

b) g(f(3))

2. Let f(x)=x2+2 and g(x)=square root of 1-x2.

a) Find the domain and range of f and g.

b) Are the functions of f g and g f defined?

3. Given F(x)=cubed root of x+5, find functions f and g such that F=f g. Explain the answer.

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Functions of functions are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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