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Let us assume two curve

$C_1:y=\frac{x}{1+x}$

$C_2:y=\frac{1}{1+\frac{1}{x}}$

Find the domain of each curve

My approach is as follow

for $C_1$ $x\ne -1$ and for $C_2, x\ne-1,0$

Hence for $C_1$ the domain is $x \in (-\infty,-1) \cup (-1,\infty)$

Hence for $C_2$ the domain is $x \in (-\infty,-1) \cup (-1,0) \cup (0,\infty)$

I agree to it theoretically but if check the value at $x=0$ for $C_2$ it shows that $y=0$ in desmos.com so I would like to verify it

Samar Imam Zaidi
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1 Answers1

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Your result is correct. For $C_2$, the value of $y$ at $x=0$ is not defined. Desmos probably simplifies the expression for $C_2$ to the one in $C_1$, but the two expressions are not interchangeable (well, they are, for $x\neq 0$, but they are not interchangeable for all $x$).

5xum
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