Question

function help me friends.... [f(x)]^3=?

Answer 1

$\displaystyle f(x) = x + \frac{1}{x}$

$\displaystyle \therefore [f(x)]^3 = (x + \frac{1}{x})^3$

$\displaystyle [f(x)]^3 = x^3 + \frac{1}{x^3} + 3\cdot x^2 \cdot \frac{1}{x} + 3 \cdot x \cdot \frac{1}{x^2}$

$\displaystyle [f(x)]^3 = x^3 + \frac{1}{x^3} + 3x + \frac{3}{x}$

$\displaystyle [f(x)]^3 = \{ x^3 + \frac{1}{x^3} \} + 3 \cdot \{ x + \frac{1}{x} \}$

$\displaystyle \therefore [f(x)]^3 = f(x^3) + 3 \cdot f(x)$

$\displaystyle \text{The function } f(x) \text{ is a function such that } f(x) = f(\frac{1}{x})$

$\displaystyle \therefore \text{ The answer is (a) } f(x^3) + 3f(\frac{1}{x})$