What is the domain of the function?

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1 Answer
Jarob R G.
Apr 8, 2018

#x in (-infty, infty)#
#y in (infty, 0)cup(0, infty)#

Explanation:

Recall that the domain is the set of valid inputs to the function. In this case, it is the set of all pairs #(x, y)# that are valid inputs.

Also recall that, while you cannot take the square root of a negative number, you can take the cube root of a negative number. For example, #root(3)(-8) = -2#. Thus, #root(3)(x)# is valid for any value of #x#.

Additionally, #root(3)(y)# is valid for all inputs of #y#, but our function #f(x, y) = root(3)(x) / root(3)(y)# is undefined when #y = 0#, due to division by zero.

Thus, our domain is #x in (-infty, infty)#, #y in (-infty,0)cup(0, infty)#.

Note: This can be more concisely written as #D = {(x, y) in bbZtimesbbZ: y != 0}#.

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