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Can't we just simplify f(x) and treat it same as that of g(x)?

Sahil
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3 Answers3

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For two functions to be identical, first condition is that their domain must be same.

What are the domains of $f(x)$ and $g(x)$?

Jaideep Khare
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    domains are different for those two functions, f(x) has all real number except 2 and g(x) has all real numbers as its domain. That concludes, both are not same function, doesn't it? – Sahil Dec 04 '17 at 06:34
  • @Nature Exactly. You're correct. – Jaideep Khare Dec 04 '17 at 07:21
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The functions $f=\frac{x^2-4}{x-2}$ and $g(x)=x+2$ are identical except at $x=2$. The graph of function $f$ has a hole at $x=2$ while $g$ is continuous. So from calculus point of view, $g$ is "nicer" than $f$ as $g$ is differentiable everywhere while $f$ is not.

BR Pahari
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$f(x)$ is completely identical to $g(x)$ for $x\neq 2$

NOTE

you can always define $f(2)=4$ as $x=2$

in this case the new $f$ is continuous

E.G. think to $\frac{\sin x}{x}$ at $x=0$

user
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