Question

Let $f\left(x\right)=(1+x^2)$ sgn x and $g\left(x\right)=f^{-1}\left(x\right)$. The correct statement of the following is :

• A. g is discontinuous at x = 1, 6, 1
• B. g is discontinuous at x = 0 only
• C. g is discontinuous at x = 1, 1 only
• D. g (x) is continuous every where in it domain.

Answer 1

The correct option is D g (x) is continuous every where in it domain.

g(x) is not defined x = 1, hence no quational and dis con. at point which do not belong to domain. x = 0 is isolated point, with no neighbor hood, by defining function alway continuous such point.
Hence g(x) is contain in it entire domain $(-\infty ,1)\cup 0\cup (1,\infty )$.