What is the domain and range of #y=ln(x^2)#?

1 Answer
Apr 9, 2017

Answer:

Domain for #y=ln(x^2)# is #x in R# but #x!=0#, in other words #(-oo,0)uu(0,oo)# and range is #(-oo,oo)#.

Explanation:

We cannot have logarithm of a number less than or equal to zero. As #x^2# is always positive, only value not permissible is #0#.

Hence domain for #y=ln(x^2)# is #x in R# but #x!=0#, in other words #(-oo,0)uu(0,oo)#

but as #x->0#, #ln(x^2)->-oo#, #y# can take any value from #-oo# ao #oo# i.e. range is #(-oo,oo)#.