What is the domain and range of #f(x) = ln(-x + 5) + 8#?

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Answer 1 · 2018-04-29T13:27:21

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

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

For the natural log,

#-x+5>0#

Therefore,

#x<5#

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

#lim_(x->-oo)y=+oo#

#lim_(x->5)y=-oo#

The range is # y in (-oo, +oo)#

graph{ln(5-x)+8 [-47.05, 17.92, -10.28, 22.2]}