First slide

Functions (XII)

Question

The function
$f (x) = \cot^{- 1} (\sqrt{(x + 3) x}) + \cos^{- 1} (\sqrt{x^{2} + 3 x + 1})$ is defined on the set S, then S is equal to

Moderate

A

{-3, 0}
B

[-3, 0]
C

[0, 3]
D

(-3, 0)

Solution

For the two components to be meaningful, we must have
$x (x + 3) \geq 0 a n d 0 \leq x^{2} + 3 x + 1 \leq 1$
Hence,
$(x + 3) x = 0 i . e ., x = 0, - 3 ∴ S = {- 3, 0}$

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