Discussion

Question:

A function f is defined by f(x) = x + $\frac{1}{x}$ . Consider the following.

Which of the above is/ are correct?

Explanation:

f(x²) = x² + $\frac{1}{x^{2}}$

(f(x))² = ${(x + \frac{1}{x})}^{2}$ = x² + $\frac{1}{x^{2}}$ + 2 = f(x²) + 2

∴ Statement 1 is true.

(f(x))³ = x³ + $\frac{1}{x^{3}}$ + 3 $(x + \frac{1}{x})$ = f(x³) + 3f(x)

∴ Statement 2 is true.

Thus both 1 and 2 are correct

Hence, option (c).

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