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Standard Formulae - 1

Let f : R →[0...

Question

$L e t f : R \to [0. \frac{π}{2}) b e d e f i n e d b y f (x) = T a n^{- 1} (x^{2} + x + a) . T h e n t h e s e t o f v a l u e s o f a f o r w h i c h f i s o n t o i s$

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Solution

The correct option is B
$x^{2} + x + a \geq 0 \Rightarrow 1 - 4 a \leq 0$

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T h e r a n g e o f f (x) = t a n^{- 1} (x^{2} + x + a) \forall x ϵ i s a s u b s e t o f [0, \frac{π}{2}) t h e n r a n g e o f a i s

f : R \to [0, \frac{π}{2})

f (x) = t a n^{- 1} (x^{2} + x + a)

a

f

f (x) = t a n^{- 1} (x^{2} + x + a)

\forall x ϵ

[0, \frac{π}{2})

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