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

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Answer 1 · 2018-01-14T00:29:05

domain: $x<10$
range: $RR$

$ln(x)$ 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]}

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