Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let f = {x,x^2/1+x^2 : x belongs to R } R be a function from R into R. Determine the range of f.

Q6  Let

  f = \left \{ \left ( x , \frac{x^2}{1+ x^2} \right ) : x \epsilon R \right \} 
R be a function from R into R. Determine the range
of f.

Answers (1)

best_answer

Given function is 
f = \left \{ \left ( x , \frac{x^2}{1+ x^2} \right ) : x \epsilon R \right \}
Range of any function is the set of values obtained after the mapping is done in the domain of the function. So every value of the codomain that is being mapped is Range of the function.
Let's take
 y = \frac{x^2}{1+x^2}
\Rightarrow y(1+x^2)=x^2
\Rightarrow y+yx^2=x^2
\Rightarrow y=x^2(1-y)
\Rightarrow x^2= \frac{y}{1-y}
\Rightarrow x= \pm \sqrt{\frac{y}{1-y}}
Now, 1 - y should be greater than zero and y should be greater than and equal to zero for x to exist because other than those values the x will be imaginary
Thus, 1 - y > 0 , y < 1 \ and \ y \geq 0
Therefore,
Range of given function is  [0,1)

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question