KCET · Maths · Functions
If \(f(x)\) and \(g(x)\) are two functions with \(g(x)=x-\frac{1}{x}\) and \(f \circ g(x)=x^3-\frac{1}{x^3}\), then \(f^{\prime}(x)\) is equals to
- A \(3 x^2+\frac{3}{x^4}\)
- B \(x^2-\frac{1}{x^2}\)
- C \(1-\frac{1}{x^2}\)
- D \(3 x^2+3\)
Answer & Solution
Correct Answer
(D) \(3 x^2+3\)
Step-by-step Solution
Detailed explanation
Here, \(g(x)=x-\frac{1}{x}\)
\(\begin{aligned} & f \circ g(x)=x^3-\frac{1}{x^3}=\left(x-\frac{1}{x}\right)^3+3 x \cdot \frac{1}{x}\left(x-\frac{1}{x}\right) \\ & f \circ g(x)=\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right) \\ & \therefore f(x)=x^3+3 x \\ & f^{\prime}(x)=3 x^2+3\end{aligned}\)
\(\begin{aligned} & f \circ g(x)=x^3-\frac{1}{x^3}=\left(x-\frac{1}{x}\right)^3+3 x \cdot \frac{1}{x}\left(x-\frac{1}{x}\right) \\ & f \circ g(x)=\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right) \\ & \therefore f(x)=x^3+3 x \\ & f^{\prime}(x)=3 x^2+3\end{aligned}\)
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
- \( \sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}= \)KCET 2019 Easy
- If \(f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x\), where \([x]=\) greatest integer \(\leq x\), then which of the following is not true?KCET 2025 Medium
- If \(\sin 3 \theta=\sin \theta\), how many solutions exist such that \(-2 \pi < \theta < 2 \pi\) ?KCET 2007 Medium
- If \(\mathrm{A}=\frac{1}{\pi}\left[\begin{array}{ll}\sin ^{-1}(\mathrm{x} \pi) & \tan ^{-1}\left(\frac{\mathrm{x}}{\pi}\right) \\ \sin ^{-1}\left(\frac{\mathrm{x}}{\pi}\right) & \cot ^{-1}(\pi \mathrm{x})\end{array}\right] \mathrm{B}=\left[\begin{array}{cc}-\cos ^{-1}(\mathrm{x} \pi) & \tan ^{-1}\left(\frac{\mathrm{x}}{\pi}\right) \\ \sin ^{-1}\left(\frac{\mathrm{x}}{\pi}\right) & -\tan ^{-1}(\pi x)\end{array}\right]\) then \(\mathrm{A}-\mathrm{B}\) equal toKCET 2016 Medium
- The area bounded by the curve \(x=4-y^{2}\) and the \(Y\)-axis isKCET 2007 Hard
- The general solution of \(|\sin x|=\cos x\) is (when \(\mathrm{n} \in \mathrm{I}\) ) given byKCET 2008 Easy
More PYQs from KCET
- Two thin biconvex lenses have focal lengths \(f_{1}\) and \(f_{2}\). A third thin biconcave lens has focal length of \(f_{3}\). If the two biconvex lenses are in contact, then the total power of the lenses is \(P_{1}\). If the first convex lens is in contact with the third lens, then the total power is \(P_{2}\). If the second lens is in contact with the third lens, the total power is \(P_{3}\), thenKCET 2021 Hard
- Ten identical cells each emf \(2 \mathrm{~V}\) and internal resistance \(1 \Omega\) are connected in series with two cells wrongly connected. A resistor of \(10 \Omega\) is connected to the combination. What is the current through the resistor?KCET 2023 Medium
- Match the physical quantities given in List-I with dimensions expressed in terms of mass (M), length (L), time (T) and electric current (A) given in List-II.
Codes:List-I List-II (a) Torque (i) \([M^{-1}L^{-2}T^{4}A^{2}]\) (b) Gravitational constant (ii) \([M^{1}L^{2}T^{-1}]\) (c) Capacitance (iii) \([M^{-1}L^{3}T^{-2}]\) (d) Planck's constant (iv) \([M^{1}L^{2}T^{-2}]\) KCET 2026 Medium - For which one of the following mixtures is composition uniform throughout?KCET 2024 Easy
- In Young's double slit experiment, how many maxima can be seen on a screen (including central maxima) if \(d = \dfrac{5\lambda}{2}\) (where \(\lambda\) is wavelength of light and \(d\) is distance between the two slits).KCET 2026 Medium
- The mass of \( \mathrm{AgCl} \) precipitated when a solution containing \( 11.70 \mathrm{~g} \) of \( \mathrm{NaCl} \) is added to a
solution containing \( 3.4 \mathrm{~g} \) of \( \mathrm{AgNO}_{3} \) is [Atomic mass of \( \mathrm{Ag}=108 \), Atomic mass of \( \mathrm{Na}=23 \) ]KCET 2019 Medium