Author: misamaliraza94
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What are Complex Numbers?
A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value ‘a’ is called the real part which is denoted by Re(z), and ‘b’ is called the imaginary part Im(z). Also, ib…
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Complex Number
Complex numbers are helpful in finding the square root of negative numbers. The concept of complex numbers was first referred to in the 1st century by a greek mathematician, Hero of Alexandria when he tried to find the square root of a negative number. But he merely changed the negative into positive and simply took the…
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Limits
Limits Limits in maths are defined as the values that a function approaches the output for the given input values. Limits play a vital role in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity. It is used in the analysis process, and it always concerns the behavior of the function at…
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Types of Functions
Functions in math have paramount importance and let us study different types of functions. We have four functions based on the mapping of elements from set A to set B. f: A → B is said to be one-to-one or injective, if the images of distinct elements of A under f are distinct, i.e, for every…
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Graph of An Inverse Function
The injective function is the reflection of the origin function with reference to the line y = x, and is obtained by swapping (x, y) with the (y, x). If the graphs of two functions are given, we can identify whether they are inverses of each other. If the graphs of both functions are symmetric…
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Steps To Find An Inverse Function
The following sequence of steps would help in conveniently finding the inverse of a function. Here we consider a function f(x) = ax + b, and aim at finding the inverse of this function through the following steps. For the given function f(x) = ax + b, replace f(x) = y, to obtain y =…
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Surjective Function
A surjective function is defined between set A and set B, such that every element of set B is associated with at least one element of set A. The domain and range of a surjective function are equal. Let us learn more about the surjective function, along with its properties and examples. What Is a Surjective Function? Surjective…
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Onto Function
Onto function is a function f that maps an element x to every element y. That means, for every y, there is an x such that f(x) = y. Onto Function is also called surjective function. The concept of onto function is very important while determining the inverse of a function. In order to determine if a…
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What Is Inverse Function?
The inverse of a function f is denoted by f-1 and it exists only when f is both one-one and onto function. Note that f-1 is NOT the reciprocal of f. The composition of the function f and the reciprocal function f-1 gives the domain value of x. (f o f-1) (x) = (f-1 o f) (x) = x…
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Inverse Function
Inverse function is represented by f-1 with regards to the original function f and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with…