find the range of following function: f(x)=3/(2-x2) - Maths -

Question

find the range of following function:
f(x)=3/(2-x2)

Ayush Jha · Accepted Answer

We have to find the range of,

$y = \frac{3}{2 - x^{2}}$

So,

$x^{2} y - 2 y + 3 = 0$

So for real values of x,

$D \geq 0 - 4 y (3 - 2 y) \geq 0$

We get two results from the above inequality,

$y \leq 0$ ......(1)

and,

$y \leq \frac{3}{2}$ ........(2)

Take intersection of (1) and (2) to get the range as-

$y \leq \frac{3}{2}$