If the function $f(x) = \left(\dfrac{5x - 8}{8 - 3x}\right)^{\frac{3}{2x - 4}}$, for $x \neq 2$ is continuous at $x = 2$, then the value of $f(2)$ is...

If $x^m + y^m = k, (m \neq 1)$ and $y'' = \dfrac{ax^b}{y^c}$ such that $a + b + c = 0$, then the value of k is...

If $y = \sin^{-1}\left(\dfrac{25 - x^2}{25 + x^2}\right)$, then $y'(1)$ is...

If $f(x)$ and $g(x)$ are inverse functions of each other and $f(x) = x + e^x$, then $g'(x) = $...