WBJEE · Maths · Functions
For every real number \(x \neq-1\), let \(f(x)=\frac{x}{x+1}\). Write \(f_1(x)=f(x)\) \& for \(n \geq 2, f_n(x)=f\left(f_{n-1}(x)\right)\). Then \(f_1(-2) . f_2(-2)\) \(\qquad\) must be
- A \(\frac{2^n}{1.3 .5 \ldots \ldots .(2 n-1)}\)
- B 1
- C \(\frac{1}{2}\binom{2 n}{n}\)
- D \(\binom{2 n}{n}\)
Answer & Solution
Correct Answer
(A) \(\frac{2^n}{1.3 .5 \ldots \ldots .(2 n-1)}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hint: } f(x)=\frac{x}{x+1}, \quad f_2(x)=\frac{x}{\frac{x+1}{\frac{x}{x+1}+1}}=\frac{x}{2 x+1} \\ & f_3(x)=\frac{x}{3 x+1}, \Rightarrow f_1(-2) \cdot f_2(-2) \ldots \ldots \ldots . f_n(-2) \\ & =\frac{-2}{-1} \times \frac{-2}{-3} \times \frac{-2}{-5}…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(R\) be the real line. Let the relations \(S\) and \(T\) on \(R\) be defined by \(S=\{(x, y): y=x+1,0 < x < 2\}, T=\{(x, y):(x-y)\) is an integer \(\}\). ThenWBJEE 2021 Medium
- If \(P, Q\) and \(R\) are angles of an isosceles triangle and \(\angle P=\frac{\pi}{2},\) then the value of \(\left(\cos \frac{P}{3}-i \sin \frac{P}{3}\right)^{3}+(\cos Q+i \sin Q) \\ (\cos R-i \sin R)+(\cos P-i \sin P) \\ (\cos Q-i \sin Q)(\cos R-i \sin R) \text { is }\)WBJEE 2013 Medium
- Let \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) be three real numbers such that \(\mathrm{a}+2 \mathrm{~b}+4 \mathrm{c}=0\). Then the equation \(\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0\)WBJEE 2011 Hard
- The value of \(2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}\) isWBJEE 2015 Medium
- If \(\alpha, \beta\) are the roots of the equation \(a x^2+b x+c=0\) then \(\lim _{x \rightarrow \beta} \frac{1-\cos \left(a x^2+b x+c\right)}{(x-\beta)^2}\) isWBJEE 2024 Hard
- The function \(f(x)=a x+b\) is strictly increasing for all real \(x\) ifWBJEE 2011 Easy
More PYQs from WBJEE
- Which of the following carbocations will be most stable?WBJEE 2009 Medium
- Let \(\theta\) be the angle between two vectors \(\vec{A}\) and \(\vec{B}\). If \(\hat{a}_{\perp}\) is the unit vector perpendicular to \(\vec{A}\), then the direction of \(\vec{B}-B \sin \theta \hat{a}_{\perp}\) isWBJEE 2024 Easy
- Chords AB & CD of a circle intersect at right angle at the point P. If the length of AP, PB, CP, PD are 2, 6, 3, 4 units respectively, then the radius of the circle isWBJEE 2024 Easy
- The integrating factor of the first order differential equation \(x^{2}\left(x^{2}-1\right) \frac{d y}{d x}+x\left(x^{2}+1\right) y=x^{2}-1\) isWBJEE 2017 Hard
- The value of \(\sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right), i=\sqrt{-1}\) isWBJEE 2016 Easy
- Identify the correct statement.WBJEE 2013 Easy