Question

If f(x) = sin for x ∈ (0,π/4) is invertible, where {⋅} and [⋅] represent the fractional part and the greatest integer functions, respectively, then f ⁻¹(x) is

(A) sin⁻¹x

(B) π/2 -cos^-1x

(c)  sin^-1{x}

(D)  cos^-1{x}

Answer 1

Correct option (A, B, C)

y = f(x) = sin {[x + + 5] {{{ xxx − − }}}}

= sin {x – {x – {x}}} = sin {x – {[x]}}

= sin {x – 0} = sin {x} = sin x

Since, 0 < x < π/4

 Therefore, x = sin^–1y

or  ,   f^–1 (x) = sin^–1x