If f : R → A defined as f x = t a n - 1 4 x 2 + x + 1 is surjective, then A is equal to

Open MARKS Web Download App

Search any question & find its solution

Question: Answered & Verified by Expert

If

f : R \to A

defined as

f (x) = t a n^{- 1} (\sqrt{4 (x^{2} + x + 1)})

is surjective, then

A

is equal to

MathematicsFunctionsJEE Main

Options:

A $(- \frac{π}{2}, \frac{π}{2})$
B $[0, \frac{π}{2})$
C $[\frac{π}{3}, \frac{π}{2})$
D $(0, \frac{π}{3}]$

Solution:

2663 Upvotes Verified Answer

The correct answer is:

[\frac{π}{3}, \frac{π}{2})

∵ x^{2} + x + 1= {(x + \frac{1}{2})}^{2} + \frac{3}{4}

∴ 4 (x^{2} + x + 1) \geq 3

\Rightarrow \sqrt{4 (x^{2} + x + 1)} \geq \sqrt{3}

∴

Range of

f (x)

is

[\frac{π}{3}, \frac{π}{2})

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.

Use on iOS or Desktop Download from Google Play