Question

Which of the following functions is non-periodic, here [.] and {.} denotes the greatest integer function and fractional part respectively ?

• A.
• B. sin-¹({x})
• C. sin⁻¹$(\sqrt{\sin x})$
• D. sin^-1(cos(x²))

Answer 1

Answer: (D)

sin^-1(cos(x²))

Answer 2

Period of $\frac { 2 ^ { x } } { 2 ^ { [ x ] } }$ is 1. Period of sin^-1{x} is 1.

Period of $\sin ^ { - 1 } ( \sqrt { \cos x } )$ is 2 π where as

Sin^-1(cosx²) is non-periodic.