The range of f(x) = ( 4 ^2 x ) ,, ; - < x < is - Vidyadip

MCQ

The range of $f(x) = \sec \left( {\frac{\pi }{4}{{\cos }^2}x} \right)\,,\; - \infty < x < \infty $ is

✓
$[1,\;\sqrt 2 ]$
B
$[1,\;\infty )$
C
$[ - \sqrt 2 ,\; - 1] \cup [1,\;\sqrt 2 ]$
D
$( - \infty ,\; - 1] \cup [1,\;\infty )$

✓

Answer

Correct option: A.

$[1,\;\sqrt 2 ]$

a
(a) $f(x) = \sec \left( {\frac{\pi }{4}\,{{\cos }^2}x} \right)$

We know that, $0 \le {\cos ^2}x \le 1$ at $\cos x = 0,\,$ $f(x) = 1$ and

at $\cos x = 1$, $f(x) = \sqrt 2 $

$\therefore$ $1 \le x \le \sqrt 2 $==>$x \in [1,\,\,\sqrt 2 ]$.

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