What is the domain and range of $g (x) = ln (4 - x)$ $g(x) =ln( 4 - x )$ ?

Question

3104 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-09T18:57:26

Domain: ${x|x in RR:x<4}$

Range: ${g(x)|g(x) in RR}$

Input to the natural logarithm must be positive so to find the domain:

$4-x>0$

$x<4$

${x|x in RR:x<4}$

For the range look at the end behavior, logarithm are continuous:

$x -> -oo, g(x) -> oo$

$x -> 4, g(x) -> -oo$

${g(x)|g(x) in RR}$

graph{ln(4-x) [-8.96, 11.04, -6.72, 3.28]}

What is the domain and range of g(x) =ln( 4 - x )g(x)=ln(4−x)g(x) =ln( 4 - x )?