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TS EAMCET · Maths · Functions

If \(f(x)=x-\frac{1}{x}, x \neq 0\), then \(3 f(x)=\)

  1. A \(3[f(x)]^2-f\left(x^2\right)\)
  2. B \([f(x)]^2-f\left(x^3\right)\)
  3. C \(f\left(x^3\right)-[f(x)]^3\)
  4. D \(f\left(x^3\right)-f\left(x^2\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(f\left(x^3\right)-[f(x)]^3\)

Step-by-step Solution

Detailed explanation

We have, \(f(x)=x-\frac{1}{x} \mathrm{gl}\) \(\therefore \quad(f(x))^3=x^3-\frac{1}{x^3}-3(x)\left(\frac{1}{x}\right)\left(x-\frac{1}{x}\right)\) \(=f\left(x^3\right)-3\left(x-\frac{1}{x}\right)\) \(\Rightarrow \quad(f(x))^3=f\left(x^3\right)-3 f(x)\)…