Question:
Let $f$ and $g$ be differentiable real valued functions on $[0,\infty)$. If $f$ is increasing, $g$ is decreasing and $h(x)=f(g(x))$, then $h(2026)-h(2025)$ is
Let $f$ and $g$ be differentiable real valued functions on $[0,\infty)$. If $f$ is increasing, $g$ is decreasing and $h(x)=f(g(x))$, then $h(2026)-h(2025)$ is
Show Hint
Increasing $\circ$ decreasing gives decreasing function.
Updated On: Apr 24, 2026
- greater than 1000 but less than 2000
- greater than or equal to 0
- less than or equal to 0
- greater than 2025
- greater than 2026
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
• Composition of increasing and decreasing functions
Step 1: Analyze monotonicity
\[ g \text{ decreasing} \Rightarrow g(2026) \leq g(2025) \]
Step 2: Apply $f$ (increasing)
\[ f(g(2026)) \leq f(g(2025)) \] \[ h(2026) \leq h(2025) \]
Step 3: Conclusion
\[ h(2026) - h(2025) \leq 0 \] Final Conclusion:
Option (C)
• Composition of increasing and decreasing functions
Step 1: Analyze monotonicity
\[ g \text{ decreasing} \Rightarrow g(2026) \leq g(2025) \]
Step 2: Apply $f$ (increasing)
\[ f(g(2026)) \leq f(g(2025)) \] \[ h(2026) \leq h(2025) \]
Step 3: Conclusion
\[ h(2026) - h(2025) \leq 0 \] Final Conclusion:
Option (C)
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Increasing and Decreasing Functions Questions
- The function f(x)=x5e-x is increasing in the interval
- The function \( f(x) = 6x^4 - 3x^2 - 5 \) is increasing in the set:
- The function \( f(x) = x^2(x-2) \) is strictly decreasing in
- The function \( f(x) = 2x^3 - 3x^2 - 36x + 28 \) is increasing in
- The function $f(x)=e^x-x$ is increasing in the interval:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions