Let f(x)= sin -1( sin x)+ cos -1( cos x), then which one of the following is incorrect?

Question

Let f(x)= sin -1( sin x)+ cos -1( cos x), then which one of the following is incorrect? (A) Domain of f(x) is x ∈ R. (B) Range of f ( x ) is [0, π] (C) f(x) is periodic with period equal to 2 π. (D) f ( x ) is decreasing ∀ x ∈(0,1).

Tardigrade Admin · Accepted Answer

Correct answer is (d) f ( x ) is decreasing ∀ x ∈(0,1).

Q. Let $f (x) = sin^{- 1} (sin x) + cos^{- 1} (cos x)$ , then which one of the following is incorrect?

Domain of $f (x)$ is $x \in R$ .

Range of $f (x)$ is $[0, π]$

$f (x)$ is periodic with period equal to $2 π$ .

$f (x)$ is decreasing $\forall x \in (0, 1)$ .

Correct answer is (d) $f (x)$ is decreasing $\forall x \in (0, 1)$ .

Q. Let f(x)=sin−1(sinx)+cos−1(cosx), then which one of the following is incorrect?

Domain of f(x) is x∈R.

Range of f(x) is [0,π]

f(x) is periodic with period equal to 2π.

f(x) is decreasing ∀x∈(0,1).