List of top Mathematics Questions on composite of functions

If the domain of the function
\[ f(x)=\sin^{-1}\!\left(\frac{5-x}{3+2x}\right)+\frac{1}{\log_e(10-x)} \]
is \( (-\infty,\alpha] \cup [\beta,\gamma) - \{\delta\} \), then \( 6(\alpha+\beta+\gamma+\delta) \) is equal to
Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad \text{if} \quad x = 1 \]
Let $f(x)=2 x+\tan ^{-1} x$ and $g(x)=\log _e\left(\sqrt{1+x^2}+x\right), x \in[0,3]$ Then
Let f and g be two function defined by \(f(x) =   \begin{cases}     x+1       & \quad x<0\\    |x-1|,   & \quad x \geq0   \end{cases}\) and g(x) = \(f(n) =   \begin{cases}     x+1,       & \quad x<0 \\     1,  & \quad x\geq0   \end{cases}\) Then (gof)(x) is 

Let
\(f(x)=\frac{x−1}{x+1},x∈R− \left\{0,−1,1\right\}\)
If ƒn+1(x) = ƒ(ƒn(x)) for all n∈N, then ƒ6(6) + ƒ7(7) is equal to :

Let
ƒ : R → R
be defined as f(x) = x -1 and
g : R - { 1, -1 } → R
be defined as
g(x) = \(\frac{x²}{x² - 1}\)
Then the function fog is :

Let f be a differential function satisfying
f(x) =\(\frac{ 2}{√3} \)\(∫^{√30} f(\frac{λ2x}{3})dλ,x>0 and f(1) = √3.\)
If y = f(x) passes through the point (α, 6), then α is equal to _____

Let f(x)=dfracax+bcx+d, then f∘ f(x)=x, provided that:
Let \( f \) and \( g \) be functions from \( \mathbb{R} \) to \( \mathbb{R} \) defined as

\( f(x) = \begin{cases} 7x^2 + x - 8, & x \le 1 \\ 4x + 5, & 1 < x \le 7 \\ 8x + 3, & x > 7 \end{cases} \)

\( g(x) = \begin{cases} |x|, & x < -3 \\ 0, & -3 \le x < 2 \\ x^2 + 4, & x \ge 2 \end{cases} \)
Then
If f(x)=x√(1+x²), then (f f)(x) is
If $f(x)= x^5 + 2x^3 + 3x + 1$ and $g(f(x)) = x,$ then $\frac{g(1)}{g’(1)}$ is equal to