List of top Mathematics Questions on types of functions

Find the range of \( f(x) = \log_e(4x^2 - 4x + 1) \)
Domain of the function \( f(x) = \frac{1{(x-2)(x-5)} \) is:}
Among the following four statements, the statement which is not true, for all \( n \in N \) is:
If \( f(x) = ax^2 + bx + c \) is an even function and \( g(x) = px^3 + qx^2 + rx \) is an odd function, and if \( h(x) = f(x) + g(x) \) and \( h(-2) = 0 \), then \( 8p + 4q + 2r = \)?

For \( n \in \mathbb{N} \), the largest positive integer that divides \( 81^n + 20n - 1 \) is \( k \). If \( S \) is the sum of all positive divisors of \( k \), then find \( S - k \).

Find the domain of the real valued function: \[ f(x) \;=\; \sqrt{\cos(\sin x)} + \cos^{-1}\left(\frac{1+x^2}{2x}\right). \]
If \( f \) is a real valued function from \( A \) onto \( B \) defined by \( f(x) = \frac{1}{\sqrt{|x| - |x|}} \), then \( A \cap B \) is:}

{If \(f(x)\) is a quadratic function such that \(f\left(\frac{1}{x}\right) = f(x) + f\left(\frac{1}{1-x}\right)\), then \(\sqrt{f\left(\frac{2}{3}\right) + f\left(\frac{3}{2}\right)} =\)}

Given the function:

\[ f(x) = \frac{2x - 3}{3x - 2} \]

and if \( f_n(x) = (f \circ f \circ \ldots \circ f)(x) \) is applied \( n \) times, find \( f_{32}(x) \).

If the real-valued function

\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]

is not defined for all \( x \in (-\infty, a] \cup (b, \infty) \), then what is \( 3^a + b^2 \)?

If \(1\cdot3\cdot5 + 3\cdot5\cdot7 + 5\cdot7\cdot9 + \ldots\) to \(n\) terms is \(n(n+1)f(n)\), then \(f(2) =\)
The range of the function \( f(x) = 8 + \sqrt{x - 5} \) is:
The number of bijective functions $f :\{1,3,5$, $7, \ldots \ldots 99\} \rightarrow\{2,4,6,8, \ldots \ldots , 100\}$, such that $f (3) \geq f (9) \geq f (15) \geq f (21) \geq \ldots f (99), $ is _____
Let \(A :\{1,2,3,4,5,6,7\}\). Define \(B=\{T \subseteq A\) : either \(1 \notin T\) or \(2 \in T \}\) and \(C = \{T _{\subseteq} A : T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set \(B \cup C\) is _______ .
If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$ and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to:
Let a∈ Z and [t] be the greatest integer t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈ (0, π) is not differentiable, is ____
Let f be a continuous function satisfying \(∫^{t ^2}_ 0 ( f ( x ) + x ^2 ) d x = \frac{4}{3} t^3 , ∀ t > 0.\) Then \(f(\frac{π^2}{4})\) is equal to 
Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.
If the local maximum value of the function f x)=\((\frac{√3e}{2 sin x} ) sin^2x ,\) \(x∈(0 ,\frac{π}{2}) \), is k/e , then  ( \(\frac{k}{ e}\) ) 8 + \(\frac{k^8}{e^ 5}\) + k 8  is equal to
Let D be the domain of the function f(x)=sin−1(\( log_{3 x} (\frac{6+2log_3x}{−5x}\))) If the range of the function g : D → R defined by g ( x ) = x − [ x ] is the greatest integer function), is ( α , β ) , then α 2 +\(\frac{ 5}{ β}\) is equal to 
Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x) = |[x] |+\(\sqrt{x -[x] }\)is discontinuous is _____.
If the local maximum value of the function f( x )=\((\frac{√3e}{2 sin x} )^{ sin^2x}\) ,\(  x ∈ ( 0,\frac{π}{2} )\),  is \(\frac{k}{e}\), then \((\frac{k}{e})^8+\frac{k^8}{e^5}+k^8 \) is equal to
Let $S=\{1,2,3,4,5,6\}$ Then the number of one-one functions $f: S \rightarrow P ( S )$, where $P ( S )$ denote the power set of $S$, such that $f(m) \subset f(m)$ where $n < m$ is _______
If \( f(x) \) satisfies the relation \( 2f(x) + f(1 - x) = x^2 \) for all real \( x \), then \( f(x) \) is:
If $f(x)=(2k + 1)x - 3 - ke^{-x } + 2e^x$ is monotonically increasing for all $x \in R$, then the least value of $k$ is