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Find each of the following functions and their domains.
f(x) = x2 - 2
g(x) = 4x - 4
(a) f g =


g f =


f f =



g g =


Find each of the following functions and their domains. f(x) = 1 - 2x
g(x) = cos(x)


f f =




(a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find a function f such that f g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
f = 1

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Find the exact value of each expression.
(a) log3(12) - log3(28) + log3(63)




(b) log4(100) - log4(32) - log4(50)




Express the given quantity as a single logarithm.
ln(4) + 2 ln(2)



Find the exact value of each expression.







Find the exact value of each expression.
(a) tan(arctan(6))


(b) sin-1(sin(7π/3))


Find the exact value of each expression.
(a) tan(sec-1(3))






Simplify the expression.
sin(tan-1(x))




Find the domain and range of the function below.
g(x) = sin-1(9x + 9)



(domain)



(range)



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