Question

State whether the given statement is true or false

Range of the function $y=\frac{3}{4-x^2}$ is
$\therefore$ Range $=[-\infty ,0]\cup [\frac{5}{4},\infty ]$

• A. True
• B. False

Answer 1

The correct option is B False

The function is not defined for $x=\pm 2.$ Also $x^2=\frac{4y-3}{y},y\ne 0$ ...(1)Since x is real $\therefore x^2=\frac{4y-3}{y}\ge 0$ or $\frac{y(4y-3)}{y^2}\ge 0$ or $4y(y-\frac{3}{4})=+ive$
$\therefore y<0$ or $y\ge 3/4$
$\therefore$ Range $=[-\infty ,0]\cup [\frac{3}{4},\infty ]$Note:0 is not included in the range by (1).