How do you find the domain and range of #arcsin(e^x)#?

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Answer 1 · 2018-08-02T02:45:41

Domain: #x in ( - oo, 0 ]#

Range: #( 0, pi/2 ]#

sin value #in [ -1, 1 ], arcsin value #in [ - pi/2, pi/2 ] and #e^x > 0,

and so,

# e^x in [ 0, 1 ] rArr x in ( - oo, 0 ]#and

#arcsin ( e^x ) in (0, pi/2 ]#

See graph, depicting these aspects.

graph{( y -arcsin(e^x))(y -pi/2)=0[-pi 0 0 pi/2]}