JEE Main 2023 (Online) 10th April Morning ShiftQuestion 1
If $f(x)=\frac{(\tan1^{\circ})x+\log_e(123)}{x\log_e(1234)-(\tan1^{\circ})}$, $x>0$, then the least value of $f(f(x))+f\left(f\left(\frac{4}{x}\right)\right)$ is
Functions
Solution
With $a=\tan1^\circ$, $f(x)=\frac{ax+b}{cx-a}$ gives $f(f(x))=x$. So the sum is $x+\frac4x\ge2\sqrt4=4$, with equality at $x=2$.