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

1 Answer
Sep 26, 2017

Answer:

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#)