Question

What should be the domain for which the function $y=\frac{x}{\sqrt{x^2-1}}$ is continuous.

• A. R
• B. R - {1}
• C. R-{0}
• D. R-[-1,+1]

Answer 1

The correct option is D

R-[-1,+1]

The important thing to know is that the fact whether a funciton is continuous or not also depends on the

domain for which the function is defined. If we define the domain such that all points of discontinuities

are excluded then we get a continuous function for the given domain.

Here,

$y=f\left(x\right)=\frac{x}{\sqrt{x^2-1}}$

y is discontinuous when $\sqrt{x^2-1}=0$

$i.e.,x=\pm 1$

$\therefore$ Domain for which f(x) is continuous is, R-[-1,-1]