List of top Mathematics Questions on Functions asked in KEAM

If $ f(x) = \log 3 - \sin x $, $ y = f(f(x)) $, find $ y(0) $.
Find the range of $ f(x) = \sqrt{x^2 + 4x + 4} $.
Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $
Given the function \( h(x) = f(g(x)) \), where \( f(x) = f'(x) = 3 \), and \( g(x) = 9 \), find \( g'(3) \), \( f'(3) \), and \( h'(3) \).
Given the function \( F(x) = |\sin(3x)| - \cos(3x) \), for \( \frac{\pi}{6} \leq x \leq \frac{\pi}{3} \), find \( f' \left( \frac{\pi}{4} \right) \).
If \( f(x) = \sqrt{x - 3} + 4 \sqrt{5 - x} \), find the domain of \( f(x) \).
Find the domain of the composite function \( f \circ g(x) \) where \( f(x) = \log(5x) \) and \( g(x) = \cos(x) \).
Let \( f(x) = 6x^2 + 9x + 10 \) and \( g(x) = x^2 - 9x - 9 \). Then the value of \( (f \circ g)(10) \) is
The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}\)  is

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) is 

Let [.]denote the greatest integer function and f(x)=[x]+[2-x],-1≤x≤4.Then
Let \(f(x)\)={-\(5,x≤0 x-5,x>0\) and \(g(x)=If(x)+2f(IxI)\).Then \(g(-2)\) will be 

Let \(f(x)=\dfrac{x-1}{x+1}\) ,Let \(S ={x∈R \text{ Iff } -1(x)=x \text{  does not hold} }\).The cardinality of S is 

The domain of the function \(f(x) = (x^2-2x-63)^{\frac{3}{2}}\), x ∈ R is
The function \(f\ \R\rightarrow\R\) given by f(x)=7-3x is
Let \(f:[-4,2] \rightarrow \R\) be given by \(f(x) = \sqrt{16-x^2}\). Then the range of the function f is
Let $f : \bullet \to \bullet $ satisfy $f (x) f ( y) = f (xy) $ for all real numbers $x$ and $y$. If $f (2)= 4$, then $f \left( \frac{1}{2} \right) = $
The range of the function $ f(x)\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} $ where $ x\in R, $ is
The domain of the function $f\left(x\right) = sin^{-1}\left(\frac{x+5}{2}\right)$ is
If $*$ is defined by $a*b$ = $a - b^2$ and $\oplus$ is defined by $\oplus$ = $a^2 + b$, where a and b are integers, then ($3 \oplus 4) * 5$ is equal to
Which one of the following functions is one-to-one?