Download App

STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
Question
Let $f: R \rightarrow R$ 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 $g(x)=f(f(f(x)))+f(f(x))$, the the greatest integer less than or equal to $g (1)$ is
✓

Answer

c
$f(x)=\left[2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right]^{\frac{1}{50}}$

$f(x)=\left[\left(2-x^{25}\right)\left(2+x^{25}\right)\right]^{\frac{1}{50}}$

$\quad=\left(4-x^{50}\right)^{1 / 50}$

$\begin{aligned} f(f(x)) =\left(4-\left(\left(4-x^{50}\right)^{1 / 50}\right)^{50}\right)^{1 / 50}=x \\ g(x)=f(f(f(x)))+f(f(x)) \\ \quad=f(x)+x \\ g(1)=f(1)+1=3^{1 / 50}+1 \\g(1)]=\left[3^{1 / 50}+1\right]=2 \end{aligned}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the area of the region $\{(x, y): x-2 y+4 \geq 0$, $\left.x+2 y^2 \geq 0, x+4 y^2 \leq 8, y \geq 0\right\}$ be $\frac{m}{n}$, where $m$ and $n$ are coprime numbers. Then $m + n$ is equal to $..........$
→
Let $x=2$ be a root of the equation $x^2+p x+q=0$ and $f(x)=\left\{\begin{array}{cc}\frac{1-\cos \left(x^2-4 p x+q^2+8 q+16\right)}{(x-2 p)^4}, & x \neq 2 p \\ 0, & x=2 p\end{array}\right.$ Then $\lim _{x \rightarrow 22^{+}}[f(x)]$ where [. ] denotes greatest integer function, is $........$
→
Let $f(\mathrm{x})=\left|2 \mathrm{x}^2+5\right| \mathrm{x}|-3|, \mathrm{x} \in \mathrm{R}$. If $\mathrm{m}$ and $\mathrm{n}$ denote the number of points where $f$ is not continuous and not differentiable respectively, then $m+n$ is equal to :
→
How many positive real numbers $x$ satisfy the equation $x^3-3|x|+2=0$ ?
→
All the letters of the word $"GTWENTY"$ are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word $"GTWENTY"$ IS
→
For a positive integer $n,\left(1+\frac{1}{x}\right)^{n}$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio, $2: 5: 12,$ then $n$ is equal to
→
$P_1$ and $P_2$ are two distinct and intersecting planes. Three non-collinear points lie on $P_1$ and another three non-collinear points lie on $P_2$ (none being on line of intersection of planes). Then the maximum number of tetrahedrons formed using these six points, is
→
The remainder when $3^{91}$ divided by $80$ is :-
→
The number of critical points of the function $f(x)=(x-2)^{2 / 3}(2 x+1)$ is :
→
If $f(x) = 2{x^3} - 3{x^2} - 12x + 5$ and $x \in [ - 2,\,4]$, then the maximum value of function is at the following value of $x$
→