Function of Single Variable in Mathematics for Mechanical and GATE Questions and Answer
The function of Single Variable Function has always been visualized as a kind of machine. So here a machine which we called f and here we gave input X and here comes a unique output Y. So every input X there is a unique output Y, But if there are more than 2 outputs then I will never call such machine a function. This uniqueness of Y is very important For Example f (x) = x 3 , Sin(x), Log(x), e x etc. Definition: Domain : Here set of input x for function f (x) is called the domain of f (x) Range : Here the set of value of f (x) for inputs x then it is called the range for function. One to One functions (Injective): Input x has a unique Output y. Onto Functions (Surjective) : when Domain is equal to the range means the number of elements in domain = number of element in range and each element in the domain has a unique output. Into Function: when Domain is not equal to range than it’s called into function. Bijective : Fun...