Let f = {(x, x²/(1 + x²); x ∈ R be a function from R into R. Determine the range of f

Solution:

It is given that f = {(x, x²/(1 + x²)); x ∈ R

In mathematics,

a function means a correspondence from one value x of the first set to another value y of the second set

Therefore,

{(0, 0), (± 0.5, 1/5), (± 1, 1/2), (± 1.5, 9/3), (± 2, 4/5), (± 3, 9/10), (± 4, 16/17)....}

The range of f is the set of all second elements.

It can be observed that all these elements are greater than or equal to 0 but less than 1

(denominator is greater than numerator).

Thus, range of f = [0, 1)

NCERT Solutions Class 11 Maths Chapter 2 Exercise ME Question 6

Let f = {(x, x²/(1 + x²) ; x ∈ R be a function from R into R. Determine the range of f

Summary:

A function f defined by f = {(x, x²/(1 + x²); x ∈ R is given. We have found that the range of f is [0, 1)