List of top Mathematics Questions on composite of functions asked in MHT CET

Let \[ f(x)=\sqrt{x^2+1}, \quad g(x)=\frac{x+1}{x^2+1}, \quad h(x)=2x-3 \] Then, \[ f'(h'(g'(x))) = ? \]

Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]

If $f(x)=\frac{3x-2}{5x+3}$ where $f:\mathbb{R}-\{-\frac{3}{5}\}\rightarrow\mathbb{R}$ is defined, then $f\circ f(1)$ is