Relations and F...

If \(A=\{-1,0,2,5,6,11\}, B=\{-2,-1,0,18,28,108\}\) and \(f(x)=x^2-x-2\). Find the value of \(f(A)\).

Find the range of the function \(\mathrm{f}(\mathrm{x})=\sqrt{20-\mathrm{x}^{2}}\).

The cartesian product \(A \times A\) has 9 elements among which are found \((-1,0)\) and \((0,1)\). Find the set \(A\) and the remaining elements of \(A \times A\).

Let \(f=\left\{\left(x, \frac{x^2}{1+x^2}\right): x \in R\right\}\) be a function from \(R\) into \(R\). Determine the range of \(f\).

If \(A=\{2,3,4\}\) and \(B=\{5,6\}\), then how many subsets does \(A \times B\) have?

A Cartesian product \(A \times B\) consists of 6 elements. If three of these are \((2,4),(4,6)\) and (5, 6), find the Cartesian set \({B} \times {A}\).

Let \(\mathrm f=\{(1,1),(2,3),(0,-1),(-1,-3)\}\) be a function from \(\mathrm{Z}\) to \(\mathrm{Z}\) defined by \(\mathrm{f(x)=a x+b}\), for some integers \(\mathrm{a, b}\). Determine \(\mathrm{a, b}\).

If \(A\) and \(B\) are two non-empty sets having n elements in common, then what is the number of common elements in the sets \(A \times B\) and \(B \times A ?\)

If \(R\) is the relation "less than" from \(A=(1,2,3,4,5)\) to \(B=(1,4,5)\), then the set of ordered pairs corresponding to \(R\) will be:

Find the domain of the function \(f(x)\) defined by \(f(x)=\sqrt{4-x}+\frac{1}{\sqrt{x^2-1}}\).