how do i find the range and domain of a fractional,polynomial.greatest integer function algebraically . What is their graphical solution and how do i judge the restrictions on them. 

Asked by laxmikant mishra | 15th Jul, 2014, 12:50: AM

Expert Answer:

Domain is the set of all values of a function that 'x' can take.

Range is the set of all values of a function that 'y' can take.

(1) Fractional function

Consider the function y equals 1 over x

In this function x can take all the values except zero.

Therefore,

x element of R minus open curly brackets 0 close curly brackets D o m a i n space o f space x space i s space R minus open curly brackets 0 close curly brackets

Now let us consider the range of f(x).

Again f(x) can take all the values except 0.

Therefore,

y element of R minus open curly brackets 0 close curly brackets R a n g e space o f space f left parenthesis x right parenthesis space i s space R minus open curly brackets 0 close curly brackets.

(2) Polynomial function

Domain of a polynomial function is the set of real numbers

And the range of polynomial function is also the set of real numbers.

In the above example, domain is the set of Real Numbers.

Range is the set of positive real numbers, including zero.

(3) Greatest integer function

Domain of greatest integer function is the set of real numbers.

Range of greatest integer function is the set of integers.

The graph of the greatest integer function is as follows:

Answered by Vimala Ramamurthy | 16th Jul, 2014, 02:43: PM