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) = x³, 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 : Function is Surjective as well as Injective.

Inverse function:  If we have f(x) = y and we inverse it means f(y) = x and both are equal then its called inverse function for example f(x) = x³ =y and now f(y) =y^1/3 = x.

GATE Question:  GATE (2007) Marks 02

If    , then y(2) = ……

a)    4 or 1

b)   4 only
c)    1 only
d)   Undefined

Answer: a) 4 or 1

Explain:

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