Question

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

(select 4)

A.
`y=cos^(-1) x`
B.
`y=cot^(-1) x`
C.
`y=csc^(-1) x`
D.
`y=sec^(-1)x`
E.
`y=sin^(-1)x`
F.
`y=tan^(-1) x`

Answer 1

A, B, E, and F

Explanation:

sinx and cosx are defined for all values of x. So, sin⁻¹x and cos⁻¹x are also defined for all values of x.

A and E are correct.

tanx is defined for all values of x.

However, tan(nπ) = 0 at when n is an integer. So, tan⁻¹(±nx) is undefined. However, tan⁻¹(-½x) is defined, because -½ is not an integer.

B and F are correct.

C and D are wrong. Both sec⁻¹x and csc⁻¹x are undefined when -1 < x < 1, and -½ is in this forbidden region.