List of top Mathematics Questions on Functions asked in AMUEEE

The number of equivalence relations on the set {1, 2, 3} containing (1, 2) and (2,1) is

Let $ A = \left\{x\in R; x\ge\frac{1}{2}\right\} $ and $ B = \left\{x\in R; x\ge\frac{3}{4}\right\} $ If $ f : A \rightarrow B $ is defined as $ f(x) = x^2 - x + 1 $ , then the solution set of the equation $ f(x) = f^{-1}(x) $ is

Let $ L $ denote the set of all straight lines in a plane. Let a relation $ R $ be defined on $L$ by $ L_1 $ $R L_2 $ if and only if the straight line $ L_1 $ is perpendicular to the straight line $ L_2 $ . Then, $ R $ is

Let $ f(x) = (x+2)^2 -2 , x \ge -2 $ . Then, $ f^{-1}(x) $ is equal to

Let $ Z $ be the set of integers. Then, the relation $R = \{ (a, b) :1 + ab > 0 \}$ on $z$ is

Let $ f : R $ - { $ \frac {5}{4} $ } $ \rightarrow R $ be a function defined as $ f(x) = \frac{5x}{4x+5} $ . The inverse of $ f $ is the map $ g : Range\,f\,\rightarrow R $ - { $ \frac {5}{4} $ } given by

Let $ * $ be a binary operation on the set $ Q $ of rational numbers defined by $ a*b $ = $ \frac{ab}{4} $ . The identity with respect to this operation is

Let a relation $ R $ in the set $N $ of natural numbers be defined by $(x, y)\Leftrightarrow x^2 - 4xy + 3y^2 = 0\,\forall\,x, y \in\,N.$The relation $ R$ is