Expressions and Functions in Grade X

Hello kids, today we are going to throw some light on the simplification of the expression and functions. In later blogs I will discuss about Composition of Functions also. You all are aware of different form of expression in grade X of Maharashtra board books; you are going to learn methods of simplifying expressions. Expressions are the mathematical phrase, in which we have finite combination of symbols that is well- formed according to rules that depend on context.  The expressions used may vary from simple to complex like from 2 + 5  to nleft.frac1k!fracd>kdt>kright|_t=0f(u(t)) + int_0>1 frac(1-t)>n n! fracd>n+1dt>n+1 f(u(t)), dt.” class=”tex” src=”http://upload.wikimedia.org/wikipedia/en/math/3/e/6/3e66d9f71339c5148097d008867d1215.png” />

Simplifying expression means, reducing the expression to the simplest form. Simplification in math is applied to different concepts and these are: simplifying radical expressions, square roots, rational expressions, fractions, exponents, algebraic expressions, complex fractions, equations and expressions. Let’s see few examples of the simplification of expression. For more information click here

1. Simplifying square root:  the process of obtaining the square root of a expression or number is termed as solving or simplifying.

Example:  Find

√48 = √(2.2.2.2.3) = 2.2√3 = √3

Determine:  √36 = √6.6 = 6.

2. Simplify rational expressions:  A rational expression is more than a fraction in which the numerator and the denominator are polynomials.

Example:

step 1: Factor the numerator and the denominator

AND

Step 2:

Divide out all common factors that the numerator and the denominator have.

1. Simplify complex fractions: If a fraction is formed with help of numerator and denominator as a fraction, then it is called as complex fraction.

Example: Simplify  Example 1:  is a complex fraction. The numerator is 3 and the denominator is 1/2.

Now, switch to the next topic that is called as simplifying expression. Term function is a relation between output and input, in which the output values depend upon input values. If there is any change in the input function then the same is reflected on the output. Let a function is f(x) = y then ‘x’ is the input and ‘y’ is the output.  when we deal with functions we also deal with other terms like, domain it is a set of all inputs, other is co-domain which is set of all outputs. Function also defines a relation between domain and co-domain.Considering two sets ‘A’ and ‘B’. We form the Cartesian product and we form relations. From all the relations, we can select a few which satisfy the rule that each element of the set A is related to only one element of the set B. When a relation satisfies this rule, it is called a function.

Now, look at an example of Simplifying Functions

Function is f(x)= x² where 0<x<5.Find the domain and range.

Solution:

Given function f(x)=x²

Domain=0,1,2,3,4

Range = 0,4,9,16

There are many different type of functions, which you are going to learn in higher grade than Grade X.  All the concepts of mathematics is very simple all you need is practice on daily basis. Nothing is impossible if you make efforts for it and even simple things become complex if you don’t do practice.

In next post we will discuss about Geometry in Grade X. Visit our blogs for more information on Math Blog on Grade X