Which one of the following function contains only one integer in its range

MATHEMATICS · Single correct · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Which one of the following function contains only one integer in its range? [Note

\operatorname{sgn}(k)

denotes the signum function of

k

.] (1)

f(x) = \frac{1}{2} \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)

(2)

g(x) = \operatorname{sgn}\left(x + \frac{1}{x}\right)

(3)

h(x) = \sin^2 x + 2 \sin x + 2

(4)

k(x) = \cos^{-1}(x^2 - 2x + 2)