Question

Let f is a function from R to R by f(x) x^2/1+x^2 where x belongs to R determine the domain and range

Answer 1

(text) here is your answer OK dude...

first I concept clear........

Domain:

For every value of x, the denominator is greater than the numerator. For x=0, the function becomes 0. So, it will accept all values and the function is never going to be undefined. Therefore Domain = R.

Range:

Since the denominator is always greater than the numerator for all values of x other than 0. And at 0 the function is =0 , the range is [0,1).

let I take your answer... ☺☺☺
Let's begin with denominator that is 1+x^2

1+x^2=0

Roots are imaginary therefore domain is R

Let y=x^2/(1+x^2)

x^2=y/(1-y)

x^2 is always positive

ie y/(1-y)>0

y takes all values [0,1)

Range is [0,1)

(/text) I hope I help you ☺☺☺