Inverse functions Topic Icon
Inverse functions

September 30, 2021

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 $$\frac{1}{f\left (x \right )}$$.

Functions Topic Icon

September 30, 2021

A function can be thought of as two sets. Let $$X$$ and $$Y$$ be two sets and $$f$$ be the function from the set $$X$$ to $$Y$ then the function $$f$$ is defined as $$ f:X\rightarrow Y$$. Here, the set $$X$$ is called the domain or the set of inputs and set $$Y$$ is the range or the set of outputs. The function $$f$$ associated with each element is $$x$$ in $$X$$ with one and only element $$y$$ in $$Y$$.

Direct and inverse proportion Topic Icon
Direct and inverse proportion

September 30, 2021

Proportion is a statement that defines two specified ratios are equal to each other. Ratio and proportion are explained using fractions. If a fraction is expressed as $$a: b$$, it is called a  ratio. On the other hand, when two ratios are equal, it is called a proportion.

Geometric sequences Topic Icon
Geometric sequences

September 29, 2021

A sequence in which every term is obtained by multiplying or dividing a particular number with the preceding number is a geometric sequence. For example, the geometric progression, $$5, 10, 15, 20, 25, \cdots$$, has a common ratio of $$5$$.

Harmonic sequences Topic Icon
Harmonic sequences

September 29, 2021

A series of numbers is in harmonic sequence if the reciprocals of all the sequence elements form an arithmetic sequence, which does not contain $$0$$. In a harmonic sequence, any terms in the sequence are considered the harmonic means of its two neighbours.

Linear inequalities Topic Icon
Linear inequalities

September 29, 2021

If in an expression, two expressions or values are written equal, then it is called an equation. For instance, $$3x+4y=12$$. On contrary to this, if an expression shows the relation between the two values with the sign ‘$$<$$’(less than), ‘$$>$$’ (greater than), ‘$$\leq$$’(less than or equal to), ‘$$\geq$$’(greater than or equal to), then it is termed as an inequality.

Linear equations Topic Icon
Linear equations

September 29, 2021

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.

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