List of top Mathematics Questions on composite of functions asked in KEAM

Let $f(x) = \dfrac{2x+3}{x-2}, \, x \in \mathbb{R}, \, x \neq 2$ and $h(x) = f(f(x))$. Then $h(h(10))$ is equal to:
Let \( f(x)=\log_5 x \, (x > 0) \) and \( g(x)=\cos^{-1}(x) \, (-1\le x \le 1) \). Then the domain of \( g \circ f \) is
Let $f(x) = 3x - 5$. The inverse of $f$ is given by
Let \( f \) and \( g \) be differentiable functions such that \( f(3)=5, g(3)=7, f'(3)=13, g'(3)=6, f'(7)=2 \) and \( g'(7)=0 \). If \( h(x) = (f \circ g)(x) \), then \( h'(3) \) is
Let \( f \) and \( g \) be differentiable functions such that \( f(3)=5, g(3)=7, f'(3)=13, g'(3)=6, f'(7)=2 \) and \( g'(7)=0 \). If \( h(x) = (f \circ g)(x) \), then \( h'(3) \) is
Let \( f \) and \( g \) be differentiable functions such that \( f(3)=5, g(3)=7, f'(3)=13, g'(3)=6, f'(7)=2 \) and \( g'(7)=0 \). If \( h(x) = (f \circ g)(x) \), then \( h'(3) \) is
Let \( f \) and \( g \) be differentiable functions such that \( f(3)=5, g(3)=7, f'(3)=13, g'(3)=6, f'(7)=2 \) and \( g'(7)=0 \). If \( h(x) = (f \circ g)(x) \), then \( h'(3) \) is
Let $f(x) = x^3$ and $g(x) = 3^x$. The values of $a$ such that $g(f(a)) = f(g(a))$ are:
If $f(x) = 3x + 5$ and $g(x) = x^2 - 1$, then $(f \circ g)(x^2 - 1)$ is equal to:
If $A = \{1, 3, 5, 7\}$ and $B = \{1, 2, 3, 4, 5, 6, 7, 8\}$, then the number of one-to-one functions from $A$ into $B$ is:}

Let \[ f(x)= \begin{cases} ax+3, & x \leq 2 \\ a^2x-1, & x > 2 \end{cases} \] Then the values of \(a\) for which \(f\) is continuous for all \(x\) are:

If $A = \{1, 3, 5, 7\}$ and $B = \{1, 2, 3, 4, 5, 6, 7, 8\}$, then the number of one-to-one functions from $A$ into $B$ is:}

Let \[ f(x)= \begin{cases} ax+3, & x \leq 2 \\ a^2x-1, & x > 2 \end{cases} \] Then the values of \(a\) for which \(f\) is continuous for all \(x\) are:

If $A = \{1, 3, 5, 7\}$ and $B = \{1, 2, 3, 4, 5, 6, 7, 8\}$, then the number of one-to-one functions from $A$ into $B$ is:}

Let \[ f(x)= \begin{cases} ax+3, & x \leq 2 \\ a^2x-1, & x > 2 \end{cases} \] Then the values of \(a\) for which \(f\) is continuous for all \(x\) are: