Here you will learn what is composition of functions with properties and examples. Let’s begin – What is Composition of Functions ? Let f : A \(\rightarrow\) B & g : f : B \(\rightarrow\) C be two functions. Then the function gof : f : A \(\rightarrow\) C defined by (gof)(x) = g(f(x)) \(\forall\) …
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 …
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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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 …
Here you will learn what is one one function with definition and examples. Let’s begin – One One Function Definition Definition : A function f : A \(\rightarrow\) B is said to be a one-one function or an injection if different elements of A have different images in B. Thus, f : A \(\rightarrow\) B …
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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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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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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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Here you will learn what is cube root function with definition, graph, domain and range. Let’s begin – Cube Root Function The function that associates a real number x to its cube root i.e. \(x^{1/3}\) is called the cube root function. Clearly, \(x^{1/3}\) is defined for all x \(\in\) R. So, we defined the cube …
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Here you will learn what is cube function with definition, graph, domain and range. Let’s begin – Cube Function Definition and Formula The function that associates a real number x to its cube i.e. \(x^3\) is called the cube function. Since \(x^3\) is defined for all x \(\in\) R. So, we defined the cube function …
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