MHT CET · Maths · Functions
If \(\mathrm{f}(x)=\log _{\mathrm{c}}\left(\frac{1-x}{1+x}\right),|x| \lt 1\), then \(\mathrm{f}\left(\frac{2 x}{1+x^2}\right)\) is equal to
- A \(2 \mathrm{f}\left(x^2\right)\)
- B \((\mathrm{f}(x))^2\)
- C \(-2 \mathrm{f}(x)\)
- D \(2 \mathrm{f}(x)\)
Answer & Solution
Correct Answer
(D) \(2 \mathrm{f}(x)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} f\left(\frac{2 x}{1+x^2}\right) & =\log _{\mathrm{e}}\left(\frac{1-\frac{2 x}{1+x^2}}{1+\frac{2 x}{1+x^2}}\right) \\ & =\log _{\mathrm{e}}\left(\frac{(1-x)^2}{(1+x)^2}\right) \\ & =2 \log _{\mathrm{e}}\left(\frac{1-x}{1+x}\right) \\ & =2 \mathrm{f}(x)\end{aligned}\)
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
- The solution of differential equation is….MHT CET 2019 Medium
- If the planes \(\bar{r} \cdot(2 \hat{i}-\lambda \hat{j}+\hat{k})=3\) and \(\bar{r} \cdot(4 \hat{i}-\hat{j}+\mu \hat{k})=5\) are paralle, then values of \(\lambda\) and \(\mu\) are respectivelyMHT CET 2022 Easy
- The equation of the plane through \((-1,1,2)\) whose normal makes equal acute angles with co-ordinate axes isMHT CET 2023 Easy
- If \(\int_0^{\frac{\pi}{3}} \frac{\tan \theta}{\sqrt{2 \mathrm{ksec} \theta}} \mathrm{d} \theta=1-\frac{1}{\sqrt{2}},(k\gt0)\), then the value of \(k\) isMHT CET 2024 Medium
- If one end of the diameter is \((1,1)\) and the other end lies on the line \(x+y=3\), then locus of centre of circle isMHT CET 2008 Medium
- If \(\frac{x^2}{\mathrm{a}}+\frac{2 x y}{\mathrm{~h}}+\frac{y^2}{\mathrm{~b}}=0\) represents a pair of straight lines and slope of one of the lines is twice that of the other, then \(a b: h^2\) is
[Note: The question has been modified to get the correct answer.]MHT CET 2024 Medium
More PYQs from MHT CET
- White light consists of wavelengths range from \(480 \mathrm{~nm}\) to \(672 \mathrm{~nm}\). What will be the wavelength range when white light is passed through glass of refractive index 1.6?MHT CET 2021 Easy
- Primary nitro alkanes are obtained in good yield by oxidising aldoximes with the help of -MHT CET 2016 Medium
- If \(A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]\), then \(A^{-1}=\)MHT CET 2021 Easy
- A weightless string can support a tension up to \(30 \mathrm{~N}\). A stone of mass \(0.5 \mathrm{~kg}\) is tied to its one end and is revolved in a circular path of radius \(2 \mathrm{~m}\) in a vertical plane. Then the maximum angular velocity of the stone will be (acceleration due to gravity \(g=10 \mathrm{~m} / \mathrm{s}^2\) )MHT CET 2022 Medium
- Glucose molecule reacts with \(' X\) ' number of molecules of phenylhydrazine to yield osazone. The value of \(X^{\prime}\) ' isMHT CET 2008 Hard
- The common name of 1-Chloro \(-2,2\) -dimethyl propane isMHT CET 2020 Medium