Some functions have a removable singularity.

Def: When the function is bounded in a neighbourhood around a singularity, the function can be redefined at the point to remove it; hence it is known as a removable singularity. In contrast, whe a function tends to infinity as z approaches 0; thus, it is not bounded and the singularity is not removable,

According to this and I found other sites that agree. Just google for removable singularity.

f(x) = sin(x) / x , f(0) is defined and is equal to 1 This is the example they all give for a removable singularity.

]]>(fg)(x) = x²+1

???

]]>You are right about the "But Not Always" example ... if I can't think of a correct example I will abandon that section.

]]>I'd also say that if f(x) = (x-3)²/(x-3) then f(3) is undefined, and we can't just simplify the function to make it x-3. There would be a limit at that point, but not a value.

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