How do you find the domain and range of f(x)= lne^(2x)?

1 Answer
Alan P.
Sep 26, 2017

Domain: x in RRcolor(white)("xxxxxx")or -oo < x < +oo
Range: f(x) in RRcolor(white)("xxx.x")or -oo < f(x) < +oo

Explanation:

ln e^color(red)a=color(red )a

So ln e^color(red)(2x)=color(red)(2x)
and
f(x)=ln e^(2x)
color(white)("xxx")rarr f(x)=2x#

f(x) is defined for all Real values of x (establishing the Domain as all RR)

Any Real value, 2x, can be established by for some Real value of x (establishing the Range as all RR)

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