JEE Main 2022 (Online) 25th June Morning ShiftQuestion 1
Let $f:\mathbf{R}\to\mathbf{R}$ be a function defined by $f(x)=\left(2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right)^{\frac{1}{50}}$. If the function $g(x)=f(f(f(x)))+f(f(x))$, then the greatest integer less than or equal to $g(1)$ is $\_\_\_\_\_\_$ .
Functions
Answer$2$
Solution
$f(x)=(4-x^{50})^{1/50}$. $f(1)=3^{1/50}$, $f(f(1))=(4-3)^{1/50}=1$, $f(f(f(1)))=f(1)=3^{1/50}$. So $g(1)=3^{1/50}+1\approx2.02$.