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

The domain of the function $f(x) = \dfrac{\log_2 (x - 5)}{x^2 + 3x - 4}$ is:

The domain of the function $f(x) = 2\sin^{-1}(2x-1) - \dfrac{\pi}{4}$ is:

The inverse of the function $f(x) = x^2 + 4x + 4, \, x \leq -2$ is $f^{-1}(x) =$

If \(f(x)+3f(1-x)=x+4\), then \(f(x)=\)

If \(f(x) = [2x]\), where \([x]\) denotes the greatest integer function in \(x\), then the image of \(\{-2.3, 2.9\}\) is

The range of the function $f(x)=\sqrt{x^{2}+4x+4}$ is:

The domain of the function $f(x)=\sqrt{x^{2}+x-2}$ is:

If \( f(x) = \frac{3^x}{3^x + \sqrt{3}} \), then \( f(x) + f(1-x) \) is equal to

The domain of the function \( f(x) = \sqrt{x - 3 + 4\sqrt{5 - x}} \) is

Let \( f(x) = \cos x \). Then the value of \( \frac{1}{2}[f(x+y) + f(y-x)] - f(x)f(y) \) is equal to

Let \( f(x) = x^2 - 10x - 19, \, x \in \mathbb{R} \). Then the inverse image of 5, \( f^{-1}(5) = \)

\(f(x) = \frac{1}{7 - \cos x},\ x \in \mathbb{R}\). Then the range of \(f\) is

The domain of the function \(f(x) = \sqrt{7 - 11x}\) is

If $f : \mathbb{R} \to \mathbb{R}$ is a function defined by $f(x) = x^2$, then which of the following is true?

The domain of definition of the function $f(x) = \frac{\log_3(x+7)}{x^2 - 5x + 6}$ is

If \( f : \mathbb{R} \to \mathbb{R} \) is a function defined by \( f(x) = \sin x \), then which of the following is true?

Let \( f:\mathbb{R} \to \mathbb{R} \) satisfy \( f(x)f(y) = f(xy) \) for all real numbers \( x \) and \( y \). If \( f(2) = 4 \), then \( f\left(\frac{1}{2}\right) \) is

Let \( f:\mathbb{R} \to \mathbb{R} \) satisfy \( f(x)f(y) = f(xy) \) for all real numbers \( x \) and \( y \). If \( f(2) = 4 \), then \( f\left(\frac{1}{2}\right) \) is

If \( f(x) = \frac{x+1}{x-1} \), then the value of \( f(f(x)) \) is equal to:

The domain of the function $f(x) = \begin{cases} \frac{x^2 - 9}{x - 3}, & \text{if } x \neq 3 \\ 6, & \text{if } x = 3 \end{cases}$ is:

If $f\left(\frac{x + 1}{2x - 1}\right) = 2x,\ x \in \mathbb{N}$, then the value of $f(2)$ is equal to:

The function $f : A \to B$ given by $f(x) = x, x \in A$, is one to one but not onto. Then:

The range of the function \( f(x) = \frac{1}{2 - \cos 3x} \) is