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

Question

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

1 Answer

Impact of this question

33367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-03T22:05:45

$x>1$ (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.

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question