If $f(x) = \frac{2x - 3}{3x - 4}$,$x \neq \frac{4}{3}$,then the value of $f^{-1}(x)$ is

Let $f(x) = (x + 1)^2 - 1$ for $x \ge -1$. Then the set $S = \{ x : f(x) = f^{-1}(x) \}$ is

If the function $f : R \to R$ is defined by $f(x) = \log_a(x + \sqrt{x^2 + 1})$,where $(a > 0, a \neq 1)$,then $f^{-1}(x)$ is

Let $R$ denote the set of all real numbers. Let $f: R \rightarrow R$ and $g: R \rightarrow (0, 4)$ be functions defined by $f(x) = \log_e(x^2 + 2x + 4)$ and $g(x) = \frac{4}{1 + e^{-2x}}$. Define the composite function $h(x) = (f \circ g^{-1})(x)$,where $g^{-1}$ is the inverse of the function $g$. Then the value of the derivative of the composite function $h(x)$ at $x = 2$ is:

Which of the following functions is the inverse of itself?

If $f(x) = 2 + |\sin^{-1} x|$ and $A = \{x \in R : f^{-1}(x) \text{ exists} \}$,then $A = $