1. ## Points of continuity

How would you find the points of continuity of this function
$\displaystyle f(x) := \frac{x^2 + 2x + 1}{x^2+1}$

2. Originally Posted by CrazyCat87
How would you find the points of continuity of this function
$\displaystyle f(x) := \frac{x^2 + 2x + 1}{x^2+1}$
If $\displaystyle f$ is continuous and $\displaystyle g$ is continuous then $\displaystyle f+g$ is continuous. Similarly, if $\displaystyle \frac{f}{g}$ is continuous if $\displaystyle g(x)\ne 0,\text{ }\forall x\in\mathbb{R}$

3. Not really sure what you meant to say here, but since both the numerator and denominator are polynomials and all polynomials are continuous, then would
$\displaystyle f(x) := \frac{x^2 + 2x + 1}{x^2+1}$ be continuous everywhere?

4. Originally Posted by CrazyCat87
Not really sure what you meant to say here, but since both the numerator and denominator are polynomials and all polynomials are continuous, then would
$\displaystyle f(x) := \frac{x^2 + 2x + 1}{x^2+1}$ be continuous everywhere?
After noting that $\displaystyle x^2+1\ne0$ then

5. haha of course!! thanks