List of top Mathematics Questions on Functions

The domain of the function \(f(x)=\frac{1}{\sqrt{|x|-x}}\) is

If \(f(x)=\{x\}\) represents the fractional part function, then for any \(x\notin \mathbb{Z}\), the expression \(f(x)+f(-x)\) is equal to...

If \(f(x)+2f(1-x)=x^{2}+5\) for all real \(x\), then \(f(x)\) is equal to...

Let \(f:R\rightarrow R\) be defined by \(f(x)=\frac{x^{2}+2x+3}{x^{2}+x+1}\). If the range of \(f(x)\) is \([a,b]\), then \(a+b=\ldots\)

The domain of function \(f(x)=\frac{1}{\sqrt{|x|-x}}\) is :

If \([\cdot ]\) represents the greatest integer function of less than or equal to type then the solution set of the equation \([x]^{2}-5[x]+6=0\) is

If \(f(x)=\sin ^{-1}\left[\log _{1/2}\left(\frac{x^{2}}{2}\right)\right]\), then the domain of the function \(f(x)\) is:

The Range of the function \(y=\log (\sin x)\), defined for all \(x\) such that \(\sin x>0\) is ...

If $f(x)=\begin{cases}\frac{x}{|x|}when~x\ne0\\ |x|when~x=0\end{cases}$ is a real valued function, then}

If \(f(x) = \frac{2x-1}{x+5}\), \(x\neq -5\) then \(f^{-1}(x)\) is equal to

The domain of the function \(f(x) = \sqrt{x-1}+\sqrt{6-x}\) is...

The domain of the function \(f(x) = ^{(10-x)}C_{(x-6)}\) is...

If \(g(x) = 1-\sqrt{x}\) and \(f(g(x)) = 5+4\sqrt{x}+x\), then the value of \(f(6)\) is...

If \(f(x) = x^2\) and \(g(x) = [x^2]\) where \([\cdot ]\) represents the greatest integer function then, \((f\circ g)(\frac{3}{2})+(g\circ f)(\frac{3}{2})\) is equal to ...

The domain of the function \(f(x) = \sqrt{\frac{x}{1+x}}\) is \(\ldots\)

Let \(f(x) = ax+b\) and \(g(x) = cx+d\). The condition \(f(g(x)) = g(f(x))\) holds for all \(x\) if and only if ...

If \(f:R\rightarrow R\) and \(g:R\rightarrow R\) are defined as \(f(x) = 2x-|x|\) and \(g(x) = 2x+|x|\), then

If \(f(x-y)+f(x+y) = 2f(x)f(y)\) for all \(x,y\in R\), then \(f(x)\) is .....

If \(g(x)\) is the inverse function of \(f(x)\), where \(f(x) = \frac{5x+3}{4x-1}\), then \(g(1) =\)

The domain of the function \(f(x) = e^{\sqrt{5x-3-2x^2}}\) is

The domain of the function \(f(x) = \sqrt{x-1}+\sqrt{3-x}\) is ...

The range of the function \[ f:\mathbb{R}-\{-1,1\}\to\mathbb{R}, \qquad f(x)=\frac{x^2}{1-x^2} \] is

If \(f\) is a subset of \(Z\times Z\), then which of the following is a function from \(Z\) to \(Z\)?

फलन f : R $\rightarrow$ R को f(x) = sin2(7x) − sin2(5x) से परिभाषित करें। निम्न में से कौन सा कथन सत्य नहीं है?

एक तल में स्थित सभी वृत्तों के समुच्चय को C से निरूपित कीजिए। उपसमुच्चय R $\subseteq$ C $\times$ C को निम्न द्वारा परिभाषित कीजिए:
R = {(C1, C2) $\in$ C $\times$ C $|$ C1 व C2 एक दूसरे को प्रतिच्छेद करते हैं}.
निम्न में से कौन सा कथन सत्य है?