Question

find the range of the function f(x) =x/1+x^2​

Answer 1

Answer:

Clearly, f(x) is defined for all x∈R.

So, domain (f)=R

In order to find the range of f(x) , let

y=f(x)

⇒y=xx+x2

⇒x2y−x+y=0

⇒x=1±1−4y2−−−−−−√2y

For x to be real, we must have

1−4y2≥0andy≠0⇒−12≤y≤12andy≠0

Also , y=-0 for x=0

Hence, range of f(x)=[-1/2,1/2]

Step-by-step explanation: