Find each of the following functions. f(x) = squareroot x, g(x) = 3 squareroot 1

Question

Find each of the following functions. f(x) = squareroot x, g(x) = 3 squareroot 1 - x (a) f compositefunction g State the domain of the function. (Enter your answer using interval notation.) (b) g compositefunction f State the domain of the function. (Enter your answer using interval notation.) (c) f compositefunction f State the domain of the function. (Enter your answer using interval notation.) (d) g compositefunction g State the domain of the function. (Enter your answer using interval notation.)

Explanation / Answer

f(x) = sqrt (x)

g(x) = cube root ( 1 - x)

a) f o g

sqrt ( cube root (1-x))

domain of the function is ( -infinity , 1 ]

b) gof

cube root ( 1 - sqrt x )

domain of the function is [0, infinity )

c) f o f

sqrt ( sqrt x )

domain of the function is [0, infinity )

d) g o g

cube root ( 1 - cube root ( 1 - x ))

domain is ( -infinity , + infinity )

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