Question

If the function f :R → A, which is defined as f(x) =
$\frac{ {x}^{2} }{ {x}^{2} + 1 }$
is surjective, then find A. ​

Answer 1

Answer:

surjective functions have their co domain as range so we must find this functions range

Step-by-step explanation:

Let's assume that the value of x²/x²+1=y

now yx²+y=x²

(y-1)x²+y=0

This must satisfy for all real values so

in this quadratic equation b²-4ac ≥0

-4(y-1)y≥0

(y-1)y≤0

so y€[0,1)

Range is [0,1)

So A€[0,1)

hope this helps

Answer 2

Hello,Buddy!!

Refer The Attachment ⤴️

• Therefore, A ➪ [0,1)

$\boxed{\tt{@MrSovereign}}$

Hope This Helps!!