# Algebra

## Inverse functions

Let $$X$$ and $$Y$$ be two sets, and $$f$$ be a one-to-one function defined by $$f:{X} \rightarrow Y$$ with domain $$X$$ and range $$Y$$. Then, $$f^{-1}:{Y} \rightarrow X$$ is called the inverse function. Here, $$f^{-1}\left ( x\right )$$ does not mean $$\frac{1}{f\left (x \right )}$$.

## Graphing inequalities

Graphical representation plays an important role in mathematics as it makes the overall material easy to understand for everyone.  Either they are linear or quadratic, equation or inequalities, they can be shown graphically.

## Linear equations

A linear equation can be written in different ways. An equation containing two variables x and y is said to form a linear equation in two variables. The highest degree of both the variables x and y in the equation is 1.

A quadratic equation is a polynomial equation of degree of order 2. ax^2 + bx + c is the general form of a quadratic polynomial. If we equate this polynomial to zero, we get a quadratic equation. The general form of a quadratic equation is ax^2 + bx + c = 0.

## Simultaneous equations 1

A simultaneous equation is where two algebraic expressions (typically in terms of x and y) intersect with each other. When you solve for a simultaneous equation, you are solving for both x and y. And they are co-ordinates.

In algebra, a polynomial consisting of variables and coefficients having the highest degree value of 2 is termed as a quadratic polynomial. The general form of a quadratic polynomial is ax^2+bx+c, where a, b and c are real numbers.

## Factorising algebraic expressions 1

Factorising means the breaking or the decomposition of any entity into the product of other entities. Factorising is the process of finding the factors. It is like dividing an expression into a multiplication of relevant expressions. It is the reverse of expanding.

## How to expand brackets 1

A bracket is a symbol which helps us maintain the difference between two terms. Whenever we have to differ one mathematical term from another mathematical term, we use a bracket. For easy understanding, consider a bracket as a wall, a wall parting two rooms or houses.

## Rearranging formulae 2

Rearranging complicated formulae can be considered the peak of algebra skills. If you manipulate an equation and make your required variable the subject before adding the numeric values, solving for variables becomes easy.

## Rearranging formulae 1

The ability to rearrange formulae or rewrite them is an important skill. There are four main things in rearranging a formula: Add or subtract the same quantity to both sides, and multiply or divide both sides by the same quantity.

## Algebraic indices

An index is used to show how many times a number is multiplied by itself. The plural word for index is indices. If some number is raised to some power, then the power it is raised to is the index of that number.

## Algebraic substitution 1

Substitution is the procedure of putting one thing like a number, a letter or symbol in place of other. In simple words, whenever we use numbers at the position of letters, it is called the substitution process.