COMEDK · Maths · 24. Functions
If \(2 f\left(x^2\right)+3 f\left(\frac{1}{x^2}\right)=x^2-1, \forall x \in R-\{0\}\), then \(f\left(x^8\right)\) is equal to
- A \(\frac{\left(1-x^8\right)\left(2 x^8+3\right)}{5 x^8}\)
- B \(\frac{\left(1+x^8\right)\left(2 x^8-3\right)}{5 x^8}\)
- C \(\frac{\left(1-x^8\right)\left(2 x^8-3\right)}{5 x^8}\)
- D None of these
Answer & Solution
Correct Answer
(A) \(\frac{\left(1-x^8\right)\left(2 x^8+3\right)}{5 x^8}\)
Step-by-step Solution
Detailed explanation
Replacing \(x\) by \(\frac{1}{x}\), we get On multiplying Eq. (i) by 2, Eq. (ii) by 3 and then subtracting Eq. (i) from Eq. (ii), we get…
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
- If \(A=\left|\begin{array}{lll}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3}\end{array}\right|\) and \(B=\left|\begin{array}{ccc}c_{1} & c_{2} & c_{3} \\ a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3}\end{array}\right|\) thenCOMEDK 2019 Medium
- The solution of differential equation
\(\frac{d y}{d x}-\frac{\cos ^2 y}{\sqrt{1-x^2}}=0\)COMEDK 2024 Medium - If for \(\mathrm{a}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}, \mathrm{b}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\mathrm{c}=-3 \hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\), then find [a b c \(]\).COMEDK 2021 Easy
- Given that, \(P(A)=0.1, P(B \mid A)=0.6\) and \(P\left(B \mid A^{C}\right)=0.3\) what is \(P(A \mid B)=\) ?COMEDK 2014 Easy
- The expression \(\dfrac{1 - \tan^2\left(\dfrac{\pi}{4} - A\right)}{1 + \tan^2\left(\dfrac{\pi}{4} - A\right)}\) equalsCOMEDK 2026 Easy
- Which one of the following equations has no solution?COMEDK 2016 Easy
More PYQs from COMEDK
- A star is moving away from the earth with speed
v. Change in wavelength \(d \lambda\) observed on earth isCOMEDK 2016 Medium - In a triangle ABC the coordinate of the vertex A is \((1,2)\). Equations of the median through B and C are respectively \(x+y=5\) and \(x=4\). Then the equation of side \(\mathrm{A B}\) isCOMEDK 2025 Medium
- Current in a conductor is expressed as \(I = 8t^3 + 3t^2 + 1\), where current I is measured in amperes and time t is measured in seconds. What is the charge that flows through a cross-section of the conductor between time t = 1s to t = 2s?COMEDK 2026 Easy
- The maximum value of \(P=500 x+400 y\) for the given constraints \(x+y \leq 200, \quad x \geq 20, \quad y \geq 4 x, \quad y \geq 0\) isCOMEDK 2024 Medium
- If \(\theta\) is the polarising angle for a medium in which the speed of light is \(v\), then according to
Brewster's lawCOMEDK 2012 Easy - - Solar spectrum is an example forCOMEDK 2018 Easy