Question #a666b

1 Answer
Jan 29, 2018

The domain is #x in RR#. The range is #y in [0, +oo)#

Explanation:

Let #y=ln(sqrt(x^2)+1)#

First check for the square root function

#x^2>0#, #AA x in RR#

and

#sqrt(x^2)+1>0#, #AA x in RR#

Therefore,

The domain is #x in RR#

When #x=0#, #=>#, #y=ln(0+1)=0#

And the function #lnx>0#, #AA x in (0, +oo)#

But here, we have

#ln(sqrt(x^2)+1)#

And

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

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

Therefore,

The range is #y in [0, +oo)#