Question

If value of x which satisfy equation ${\cos }^{-1}x>{\cos }^{-1}{x}^2$ is $xϵ[a,b)$.
Find the value of a and b.

• A. $a=-2,b=-1$
• B. $a=-1,b=0$
• C. $a=0,b=1$
• D. $a=1,b=2$

Answer 1

The correct option is B $a=-1,b=0$

${\cos }^{-1}x>{\cos }^{-1}{x}^2$
or $x<x^2$ ($\because {\cos }^{-1}$ is decreasing)
or $x^2-x>0$
or $x(x-1)>0$
$\Rightarrow$ $xϵ[-1,0)$