What is Domain and range of: ln {x} ?

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Answer 1 · 2018-05-28T02:36:06

Domain: #(0,+oo)# Range: #(-oo,+oo)#

Let #f(x) = ln(x)#

#f(x)# is defined #forall x > 0#

Hence, the domain of #f(x)# is #(0,+oo)#

Consider #lim_(x->0) f(x) -> -oo#

and #lim_(x->+oo) f(x) -> +oo#

Hence, the range of #fx)# is #(-oo,+oo)#

We can visualise these results from the graph on #lnx# below.

graph{lnx [-10, 10, -5.005, 4.995]}