Good afternoon, students, welcome to second class of functions. In first class, we talked about the

domain of functions, we talked about how to solve different inequalities. We also learnt that how to

solve functions of modular questions. Then we also learnt about domain also. Now, we will study

further.

We ended the class with domain, what is domain of a functions? If y is equal to f(x) has been

expressed as mathematical expression and domain has not been stated explicitly then it is

considered to be largest set of x values for which y is real. The largest set of X value for which y is

real that set is called Domain.

Today, we will talk about what is range of functions. What is range of functions? The set of values of

y that we obtain after inputting domain. After putting domain in the functions which gives the set of

values of y, we call it as range. After putting domain values when we get the set of values of y, we

call it as range.

Let me give you few examples. Say, y is equal to x square, what is it’s domain? If nothing is written

then domain is all x for which y is defined. Y is defined for all x belonging to real numbers. So,

domain is x belong to real numbers. After putting real numbers then what all values of y we will get.

We can see here clearly that if y is minimum zero because square of anything can never be negative.

Square of anything will be always non-negative. It will never be negative, so minimum value of y is

zero, maximum value of y approaches to infinity. Hence, y belongs to zero to infinite. Y can take all

the values between zero and infinity. Hence, range of this function is y belong to zero to infinity,

what is this – range.

Let us take one more example. What is range of y equal to 1 plus x square? What will be the range

of y is equal to x square? Here minimum value of y will be 1 because x square minimum is zero,

hence minimum value of y will be 1. Hence, minimum value of y is 1 and maximum value is infinite,

then y belongs to 1 to infinite.

Let us solve a question, you know all the basics. This was just for revision, let us solve the question.

Question is, find the range y equals to 7 minus xP x minus 3? Find the range y equals to 7 minus xp x

minus 3? Let us discuss what is its domain? First let us talk about what is its domain?