Question

$2\sqrt{2}cosx$ --sinx $+4$

• A. $\le 1$
• B. $=1$
• C. $\ge 1$
• D. 2

Answer 1

Answer: (C)

$\ge 1$

concept - $f\left(x\right)=asinx\pm bcosxxϵR$
range of $f\left(x\right)ϵ[-\sqrt{a^2+b^2},\sqrt{a^2+b^2}]$
by using concept,
$f\left(x\right)=2\sqrt{2}cosx-sinx$
range of $f\left(x\right)ϵ[-3,3]$
$\therefore g\left(x\right)=f\left(x\right)+4$
$\therefore$ range of $g\left(x\right)ϵ[1,7]$

$\therefore g\left(x\right)\ge 1.$