Question

What is the domain and range of `f(x) = ln (10-x)`?

Answer 1

domain: `x<10`
range: `RR`

Explanation:

`ln(x)` graph: graph{ln(x) [-10, 10, -5, 5]}
the natural log function only outputs a real number if the input is greater than 0.

this means the domain is `10-x>0`
`x<10`

the natural log function can output any real number, so the range is all real numbers.

check with this graph
`f(x)=ln(10-x)` graph{ln(10-x) [-10, 10, -5, 5]}