\(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 3x + 4 = 0\). Find \(\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\)

A binary operation \(\Delta\) is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}{\sqrt{ab}}\), where a\(\neq\) 0, b\(\neq\) 0. Evaluate \...

Given that \(f(x) = \frac{x+1}{2}\), find \(f^{1}(-2)\).

Simplify \(\frac{1}{(1-\sqrt{3})^{2}}\)

The function f: x \(\to \sqrt{4 - 2x}\) is defined on the set of real numbers R. Find the domain of f.

If \(log_{y}\frac{1}{8}\) = 3, find the value of y.

If \(x^{2} - kx + 9 = 0\) has equal roots, find the values of k.

Find the coordinates of the centre of the circle \(3x^{2}+3y^{2} - 4x + 8y -2=0\)

Given that \(\frac{6x+m}{2x^{2}+7x-15} \equiv \frac{4}{x+5} - \frac{2}{2x-3}\), find the value of m.