How do you find the domain and range of #f(x) = 2 / sqrt(3x-2)#?

1 Answer
James W.
Dec 15, 2017

The domain is #{x:x in R and x>2/3}# and the range is #{y:y in R and y>0}#

Explanation:

The domain is the set of values which can be passed into a function. In this case, we have the constraint:

#3x-2>=0# (since you can't have a root of a negative number)

#3x>2#
#x>2/3#

Hence, the domain is #{x:x in R and x>2/3}#

The range is the set of values which the function can produce. As #x# increases, the value of the root gets larger and #f(x)# tends towards #0#. Hence the range is #{y:y in R and y>0}#

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