Let $f(x) = 1 - \dfrac{1}{x}, g_2(x) = f(f(x)), g_3(x) = f(f(f(x)))$ and so on. If $\int x \cdot g_{2026}(x)\,dx = \int g_{2025}(x)\,dx + h(x) + c$, then $h(x) = $...

If $g(x) = 1 - \sqrt{x}$ and $f(g(x)) = 5 + 4\sqrt{x} + x$, then the value of $f(6)$ is...

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...