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Into Function – Definition and Examples

Here you will learn what is into function with definition and examples. Let’s begin – Into Function Definition Definition : A function f : A \(\rightarrow\) B is said to be an into function if every element of B having no pre-image in A. In other words, f : A \(\rightarrow\) B is an into …

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Onto Function (Surjection) -Definition and Examples

Here you will learn what is onto function with definition and examples. Let’s begin – Onto Function (Surjection) Definition Definition : A function f : A \(\rightarrow\) B is said to be an onto function if every element of B is the f-image of some element of A i.e. , if f(A) = B or …

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Many One Function – Definition and Examples

Here you will learn what is many one function with definition and examples. Let’s begin – Many One Function Definition : A function f : A \(\rightarrow\) B is said to be a many-one function if two or more elements of set A have the same image in B. Thus, f : A \(\rightarrow\) B …

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What is the formula to find number of one one function ?

Solution : If A and B are two sets having m and n elements respectively such that m \(\le\) n, then the total number of one-one functions from A to B is \(^nC_m \times m!\) where m! is m factorial. For example, Let set A have 3 elements and set B have 4 elements, then …

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Implicit and Explicit Function – Definition and Example

Here you will learn what is implicit and explicit function with definition and examples. Let’s begin – Implicit and Explicit Function Definition : A function defined by an equation not solved for the dependent variable is called implicit function. e.g. the equations \(x^3 + y^3\) = 1 and \(x^y\) = \(y^x\), defines y as an …

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What is Homogeneous Function – Definition and Example

Here you will learn what is homogeneous function definition with example. Let’s begin – What is Homogeneous Function ? Definition : A function is said to be homogeneous with respect to any set of variables when each of its terms is of the same degree with respect to those of the variables. For example, \(5x^2 …

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