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## Homework Statement

consider the function f(x) = (4 - x) / (2 - [tex]\sqrt{x}[/tex]). define a new function g(x) = f(x) for all x except 4 and such g(x) is continuous at 4.

## The Attempt at a Solution

i got the limit of the f(x) when x approches 4 and i got 4 as the final answer.

here's how i did it,

1) (4-x) / (2 - [tex]\sqrt{x}[/tex] )

2) (2 + [tex]\sqrt{x}[/tex]) (2 - [tex]\sqrt{x}[/tex]) / (2 - [tex]\sqrt{x}[/tex])

3) (2 + [tex]\sqrt{x}[/tex])

4) when we plug in 4 in the equation (2 + [tex]\sqrt{x}[/tex]), we get

(2 + [tex]\sqrt{4}[/tex]) = 4

so, g(x) = f(x) when x [tex]\neq[/tex] 4

and = (2 + [tex]\sqrt{x}[/tex]) when x = 4

now my question is is my way of approching this problem correct, and is my answer correct?

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