Relations and F...

Let \({f}: {R} \rightarrow {R}\) be defined by \({f}({x})=2 {x}+6\) which is a bijective mapping, then \({f}^{-1}({x})\) is given by,

Let A = Q × Q and let * be a binary operation on A defined by (a, b) * (c, d) = (ac, b + ad) for all (a, b), (c, d) belongs to A then find identity element in A.

Let \(\mathrm{L}\) denote the set of all straight lines in a plane. Let a relation \(\mathrm{R}\) be \(\mathrm{l R m}\) if \(\mathrm{l}\) is perpendicular to \(\mathrm{m \forall l, m \in L}\). Then \(\mathrm{R}\) is:

The identity element for the binary operation * defined on \(Q-\{0\}\) as: \(a{*} b=\frac{a b}{2}\), is:

The relation \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}\) on a set \(A=\{1,2,3\}\) is:

Which of the following functions, \(f:R \rightarrow R\) is one-one?

Let \(R\) be the set of real numbers and * be the binary operation defined on \(R\) as \(a^{*} b=a+b-a b \forall a, b \in R\). Then, the identity element with respect to the binary operation * is:

The relation 'has the same father as' over the set of children is:

If \(f(x+1)=x^{2}-3 x+2\), then what is \(f(x)\) equal to?

On the set of positive rationals, a binary operation * is defined by \(\mathbf{a} * \mathrm{b}=\frac{2 \mathrm{ab}}{5}\). If \(2{*} \mathrm{x}=3^{-1}\), then \(\mathrm{x}=?\)