Question

what will be the range of 1/1-x2.please telllllllll<br />​

Answer 1

Answer:

The range is : y < 0 and y ≥ 1

Step-by-step explanation:

The denominator is 1 - x²

∀x ∈ R, 1 + x² > 0

Therefore,

The domain of f(x) is x ∈ R

To determine the range, proceed as follows

y = (1/1 - x²)

⇒ y(1 - x²) = 1

⇒ y - yx² = 1

⇒ -yx² = 1 - y

⇒ yx² = y - 1

⇒ x² = (y - 1)/y

⇒ x = √(y - 1)/y

The range of  f ( x )  is the domain of  x

(y - 1)/y > 0

y ∈ R*

⇒ y - 1 ≥ 0

⇒ y < 0 and y ≥ 1

Therefore,

The range is : y < 0 and y ≥ 1

Hope it helps!