The range of the function $f(x)=\frac{1}{1-x^2}, x ≠±1$ is :

(-∞, 0] ∪ (1, ∞) (-∞, 0] ∪ [1, ∞) (-∞, 0) ∪ (1, ∞) (-∞, 0) ∪ [1, ∞)

(-∞, 0) ∪ [1, ∞)

The correct answer is Option (4) → $(-∞, 0) ∪ [1, ∞)$ $f(x)=\frac{1}{1-x^2},y=\frac{1}{1-x^2}$ so $\frac{1}{y}=1-x^2$ $x^2=\frac{y-1}{y}$ $⇒x=\sqrt{\frac{y-1}{y}}$ $⇒y∈R-[0,1)$ $≡y∈(-∞, 0) ∪ [1, ∞)$