TS EAMCET · Maths · Functions
If \(f(x)=x-\frac{1}{x}, x \neq 0\), then \(3 f(x)=\)
- A \(3[f(x)]^2-f\left(x^2\right)\)
- B \([f(x)]^2-f\left(x^3\right)\)
- C \(f\left(x^3\right)-[f(x)]^3\)
- D \(f\left(x^3\right)-f\left(x^2\right)\)
Answer & Solution
Correct Answer
(C) \(f\left(x^3\right)-[f(x)]^3\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)=x-\frac{1}{x} \mathrm{gl}\) \(\therefore \quad(f(x))^3=x^3-\frac{1}{x^3}-3(x)\left(\frac{1}{x}\right)\left(x-\frac{1}{x}\right)\) \(=f\left(x^3\right)-3\left(x-\frac{1}{x}\right)\) \(\Rightarrow \quad(f(x))^3=f\left(x^3\right)-3 f(x)\)…
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