Math. 69.104A

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1. Let f(x) = (x^2)sin(x^2 - 1) and let g(x) = Sqrt(x + 1). What is the form of the composition of f with g, i.e., what is (f o g)(x)??

sin(x)

(x+1)sin(x^2 - 1)

(x+1)sin(x)

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2. What is the form of the inverse function, F(x), of f(x)=(2x+3)/(2x-3)??

F(x) = -1

F(x) = (3+3x)/(2x-2)

F(x) = (2x-3)/(2x+3)

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3. What is the domain of F, Dom(F), for the inverse function F you found in (2) above?

(3/2, inf)

all real numbers x different from 1

(-inf, 1)

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4. On which one of the following intervals does the function f(x)= sin(x) / x have an inverse?

(0, Pi/8)

(Pi, 2Pi)

(3Pi, 6Pi)

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