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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

  1. A \(\frac{\left(1-x^8\right)\left(2 x^8+3\right)}{5 x^8}\)
  2. B \(\frac{\left(1+x^8\right)\left(2 x^8-3\right)}{5 x^8}\)
  3. C \(\frac{\left(1-x^8\right)\left(2 x^8-3\right)}{5 x^8}\)
  4. D None of these
Verified Solution

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…