What is the domain and range of #ln(1-x^2)#?

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Answer 1 · 2018-06-06T14:30:25

Domain: #{x|-1< x <1}# or in interval notation #(-1,1)#

Range: #{y|y<=0}# or in interval notation #(-oo, 0]#

#ln(1-x^2)#

The input to the natural log function must be greater than zero:

#1-x^2>0#

#(x-1)(x+1)>0#

#-1< x <1#

Therefore Domain is:

#{x|-1< x <1}# or in interval notation #(-1,1)#

At zero the value of this function is #ln(1) = 0# and as #x->1# or as #x-> -1# the function #f(x) -> -oo# is the range is:

#{y|y<=0}# or in interval notation #(-oo, 0]#

graph{ln(1-x^2) [-9.67, 10.33, -8.2, 1.8]}