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

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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]}