Difficult
Let $f$ and $g$ be two differentiable functions on $R$ such that $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$. Then for all $x$,which of the following is true?
- A$f(g(x)) > f(g(x-1))$
- B$f(g(x)) > f(g(x+1))$
- C$g(f(x)) > g(f(x-1))$
- D$g(f(x)) < g(f(x+1))$
Explore More
Similar Questions
If $y = \sin (\sqrt {\sin x + \cos x} )$,then $\frac{dy}{dx} = $
Medium
View SolutionIf $G(x) = -\sqrt{25 - x^2}$,then $\mathop{\lim}\limits_{x \to 1} \frac{G(x) - G(1)}{x - 1} = $
Medium
View SolutionFind the derivative: $\frac{d}{dx} \left( \frac{\log x}{\sin x} \right)$
Easy
View SolutionFind the derivative of the following function: $2 \tan x - 7 \sec x$.
Medium
View Solution$\frac{d}{dx} [\operatorname{cosech}^{-1}(\tan 2x)] = $
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo