How do you find the domain and range of ln (inverse sinx)?

1 Answer
Deepak Pandey
Aug 31, 2017

Domain: #(0,1]#
Range: #(-∞,ln (pi/2)]#

Explanation:

Let #f (x)=ln (sin^-1x)#
Now as #lny# is defined only if #y>0#
#:.# For #ln (sin^-1x)# to be defined we must have
#sin^-1x>0#
Also #sin^-1x# is only defined in the interval #[-1,1]#
and #sin^-1x >0# for #x in (0,1]#
#:.# The domain of #f (x)# is #x in (0,1]#
And as #sin^-1y# and #lny# are increasing functions
#:.# The range of #f (x)# will be #(-∞,ln(pi/2)]#

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