How do you find the domain and range of #f(x) = ln(-x + 5) + 8#?

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Answer 1 · 2018-07-31T13:19:30

Domain is #(-oo,5)# and range is #(-oo,oo)#

As we can have logarithm of only a positive number, we must have

#-x+5>0# or #x<5#, which gives the domain.

The least possible value of #ln(-x+5)# is #-oo# and its maximum possible value is #oo#

Hence, range is #(-oo,oo)#.

Answer 2 · 2018-07-31T13:24:30

The domain is #x in (-oo,5)#.
The range is #y in RR#

The function is

#f(x)=ln(-x+5)+8#

The logarith function #lnx# is defined for #x>0#

Therefore,

#-x+5>0#

#x<5#

The domain is #x in (-oo,5)#

To find the range, let

#y=ln(-x+5)+8#

#ln(5-x)=y-8#

#5-x=e^(y-8)#

#x=5-e^(y-8)#

The exponential function #e^x# is defined over #RR#

Therefore,

The range is #y in RR#

graph{ln(5-x)+8 [-38, 35.07, -15.4, 21.14]}