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

If \(f(x)=\log _{e}\left(\frac{1-x}{1+x}\right)\), \(|x|\lt 1\), then \(f\left(\frac{4x}{4+x^{2}}\right)\) is equal to

If \(f(x)=\frac{2}{x+5}\) and \(g(x)=x^{2}-1\), then the positive value of \(x\) satisfying \((f\circ g)(x)=\frac{1}{10}\) is

If \(f(x) = \frac{4x+3}{6x-4}\), \(x\neq \frac{2}{3}\) and \((\text{fof})(x) = g(x)\) where \(g:R-\{\frac{2}{3}\}\rightarrow R-\{\frac{2}{3}\}\), then \((g\,o\,g\,o\,g\,o\,g\,o\,g)\,(3) =\)

If \(g(x) = x^2+x-2\) and \(\frac{1}{2}(g\circ f)(x) = 2x^2-5x+2\) then \(f(x)\) is equal to

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

If \(\mathrm{f}(x)=\log \left(\frac{1+x}{1-x}\right)\) and \(\mathrm{g}(x)=\frac{3 x+x^3}{1+3 x^2}\), then \((\mathrm{fog})(x)=\)

Let $f : \mathbb{R} - \{2\} \rightarrow \mathbb{R} - \{1\}$ defined by $f(x) = \frac{x-3}{x-2}$ and $g : \mathbb{R} \rightarrow \mathbb{R}$ defined by $g(x) = 3x - 2$, then sum of all values of $x$ for which $f^{-1}(x) + g^{-1}(x) = 19/6$ is ______.

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

If $f(x) = \frac{x}{2x+1}$ and $g(x) = \frac{x}{x+1}$, then $(f \circ g)(x) = $