Question

Help Please!(:
f(x)= (x-4)/(sqrt(x)-2)
g(x)= sqrt(x)+2

Why is f(x) and g(x) not the same function?
why can you find the limit as x approaches 4 of f(x) by finding the limit as x approaches 4 of g(x)?

Answer 1

because the domain for f(x) is all real numbers except for 4, and the domain for g(x) is all real number.

Answer 2

why can you find the limit as x approaches 4 of f(x) by finding the limit as x approaches 4 of g(x)? @sourwing

Answer 3

\[\lim_{x \rightarrow 4} = \frac{ x-4 ( \sqrt{x } + 2 )}{ (\sqrt{x} - 2) (\sqrt{x} + 2)}\]\[\lim_{x \rightarrow 4}\frac{ x -4(\sqrt{x +2)} }{ (x-4) }\]
\[\lim_{x \rightarrow 4} \sqrt{x} + 2\]

this is how it's happen... got it ?