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

Answer:

A, B, E, and F  

Step-by-step 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.