What is the domain and range of #y= ln(6-x) +2#?

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Answer 1 · 2017-06-08T20:55:33

Domain #x in(-oo,6)#
Range=#yin(-oo,(ln 6) +2)#

TO find the domain we take the values of #X# for which the function is defined.
for this the input of log cannot be negative or zero so

#6-x>0#
#x<6#

hence Domain of definition extends from
# x in(-oo,6)#

Now for range we see the graph graph{ln x [-10, 10, -5, 5]}

so putting# x=6# in graph of #y=lnx#

we get #ln6#

#yin(-oo,ln6 +2#
#yin(-oo,(ln 6) +2)#