Question

Which of the following inverse functions are defined for x=-1/2? Select all thst apply.

Y=cos ^-1x
Y= cot^-1x
Y=csc^-1x
Y=sec^-1x
Y=sin^-1x
Y=tan ^-1x

Answer 1

all but the last one I think but don't quote me

Answer 2

Function Domain

sin−1(x) [−1,1] →→→→→Defined

cos−1(x) [−1,1] →→→→→Defined

tan−1(x) (−∞,∞) →→→→→Defined

cot−1(x) (−∞,∞) →→→→→Defined

sec−1(x) (−∞,−1]∪[1,∞) →→→→→ not Defined

cosec−1(x) (−∞,−1]∪[1,∞) →→→→→not Defined

As, you can see that, all inverse trigonometric functions are defined for,
`x=(-1)/(2)`, except sec−1(x) and cosec−1(x)

, whose domain is not valid or do not exist when ,
`x=(-1)/(2)`.