Let $\left[ x \right]\;$ denote the greatest integer less than or equal to $x$. If $f\left( x \right) = {\sin ^{ - 1}}x,{\rm{g}}\left( x \right) = \left[ {{x^2}} \right]\;and\;h\left( x \right) = 2x,\frac{1}{2} \le x \le \frac{1}{{\sqrt 2 }},$ then

$hofo{\rm{g}} = ho{\rm{g}}\;of$

$fo{\rm{g}}oh\;\left( x \right) = \pi /2$

$fo{\rm{g}}oh\left( x \right) = \pi $

$hofo{\rm{g}} \ne ho{\rm{g}}\;of$

JEE MATHEMATICS MCQ: FUNCTIONS

1 Hard

1 of 1

Analyzing +4 | -1

Let

\left[ x \right]\;

denote the greatest integer less than or equal to

x

. If

f\left( x \right) = {\sin ^{ - 1}}x,\mathrm{g}\left( x \right) = \left[ {{x^2}} \right]\;and\;h\left( x \right) = 2x,\frac{1}{2} \le x \le \frac{1}{{\sqrt 2 }},

then

View answer and explanation

Correct option: C

hofo\mathrm{g} = ho\mathrm{g}\;of

Option D (

hofo\mathrm{g} = ho\mathrm{g}\;of

) is correct because after evaluating both sides, they are equal for all x in the given interval.