List of top Mathematics Questions on composite of functions asked in JEE Main

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

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 _____

If $f(x)= x^5 + 2x^3 + 3x + 1$ and $g(f(x)) = x,$ then $\frac{g(1)}{g’(1)}$ is equal to