+0

# Domain

-1
90
2
+193

There are three real numbers $x$ that are not in the domain of

$$f(x) = \frac{1}{1+\frac{1}{1+\frac 1x}}.$$

What is the sum of those three numbers?

Feb 5, 2021

#2
+113120
+1

Well we cannot divide by 0 so

$$x\ne0$$

$$1+\frac{1}{x}\ne0\\ \frac{1}{x}\ne-1\\ x\ne-1$$

$$1+\frac{1}{1+\frac{1}{x}}\ne0\\ \frac{1}{1+\frac{1}{x}}\ne-1\\ \frac{x}{x+1}\ne-1\\ x\ne -x-1\\ 2x\ne-1\\ x\ne -\frac{1}{2}$$

Feb 5, 2021