What is the domain and range of ln(x-1)?

1 Answer
Mar 3, 2018

Answer:

#x>1# (domain), #yinRR# (range)

Explanation:

The domain of a function is the set of all possible #x# values that it is defined for, and the range is the set of all possible #y# values. To make this more concrete, I'll rewrite this as:

#y=ln(x-1)#

Domain: The function #lnx# is defined only for all positive numbers. This means the value we're taking the natural log (#ln#) of (#x-1#) has to be greater than #0#.

Our inequality is as follows:

#x-1>0#

Adding #1# to both sides, we get:

#x>1# as our domain.

To understand the range, let's graph the function #y=ln(x-1)#.

graph{ln(x-1) [-10, 10, -5, 5]}

When we look at our graph, there are no discontinuities in it, thus our range is:

#yinRR#, which just means #y# is a member of the real numbers or #y# can take on any value.