How do you find the x values at which #f(x)=x/(x^2+1)# is not continuous, which of the discontinuities are removable?

1 Answer
Feb 5, 2017

#f(x)= x/(x^2+1)# is defined and continuous in all of #RR#

Explanation:

#f(x) = x/(x^2+1)#

is a rational function, that is the quotient of two polynomials. As such it is defined and continuous everywhere except where the denominator vanishes.

However as:

#x^2 + 1 >0 AAx in RR#

We can conclude that #f(x)# is defined and continuous in all of #RR#