Relations and F...

Let \(f: R-\{2\} \rightarrow R\) be defined by \(f(x)=\frac{x^2-4}{x-2}\) and \(g: R \rightarrow R\) be defined by \(g(x)=x+2\). The relation between \(f\) and \(g\) will be:

Find the domain of the function \(f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}\).

Find the domain of \(f(x)=\sqrt{4-x^2}\).

If \(A=\{a, b\}\) and \(B=\{1,2,3\}\), find the value of \((A \times B) \cap(B \times A)\).

If \(g=\{(1,1),(2,3),(3,5),(4,7)\}\) is a function and it is described by the formula, \(g(x)=\alpha x+\beta\), then what values should be assigned to \(\alpha\) and \(\beta\)?

Find the range of the function \(f(x)=\frac{3}{2-x^2}\).

If \(A=\{1,2,3, \ldots, 14\}\) and \(R\) is a relation defined on \(A\) such that \(R=\{(x, y): 3 x-y=0\) where \(x, y \in A\}\), then find the range of \(R\).

If \(f: A \rightarrow R, f(x)=x^2+1\), where \(A=\{-1,0,2,4\}\), then find the range of \(f\).

Let \(A=\{1,2,3\}\) and \(B=\{x: x \in N, x\) is prime less than 5\(\}\). Find \(A \times B\).

If \(A\) and \(B\) are the domain and range respectively for the relation \(R\) such that \(R=\{(x, x+5)\) \(: x \in\{0,1,2,3,4,5\}\}\), then which of the following option is true?