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Graphical Interpretation of Continuity

Let fx = –1si...

Question

Let $f (x) = {cot}^{- 1} (sin x) + {sin}^{- 1} (x - {x})$ , where ${x}$ denotes the fractional part function. Then

f

is one-one

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D_{f} = [- 1, 2)

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f

is many one

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R_{f} = {\frac{π}{4}, \frac{π}{2}, \frac{3 π}{4}}

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Solution

The correct option is D $R_{f} = {\frac{π}{4}, \frac{π}{2}, \frac{3 π}{4}}$
The graph of the given function is shown in the adjacent figure.
Clearly
$D_{f} = [- 1, 2)$

$R_{f} = {\frac{π}{4}, \frac{π}{2}, \frac{3 π}{4}}$ and $f$ is many-one.

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