Find the range of the following functions. i) (x)/(2+x^(2) ) 100 points for correct answers i need it ASAP, thank u ^_^

Question

Find the range of the following functions.

i)
`(x)/(2+x^(2) )`
100 points for correct answers
i need it ASAP, thank u ^_^

Answer 1

Explanation:

y = x/(2+x²)

2y + yx² = x

yx² - x + 2y = 0

(1±√(1-8y²))/2y

Now, 1 - 8y² ≥ 0

8y²≤1

y² ≤ 1/8

y ∈ (-1/2√2, 1/2√2)
Thanks