Functions: แบบฝึกหัด

Given the function \(f(x) = 4x - 3\), find the inverse function \(f^{-1}(x)\).

The function \(f\) is defined by \(f(x) = \frac{2x+3}{x-5}\) for \(x \neq 5\). Find the inverse function \(f^{-1}(x)\).

The variable \(y\) is inversely proportional to the square root of \(x\). When \(x = 16\), \(y = 3\). Find the value of \(x\) when \(y = 2\).

Find the coordinates of the points of intersection of the line \(y = 3x - 1\) and the curve \(y = x^2 + x - 9\).

Given the function \(f(x) = \frac{12}{x-3}\), state which value of \(x\) must be excluded from the domain of \(f\).

The function \(g\) is defined as \(g(x) = 5x + 2\). Find the inverse function \(g^{-1}(x)\).

The variable \(y\) is inversely proportional to the square of \(x\). When \(x = 3\), \(y = 4\). Find the value of \(y\) when \(x = 6\).