Anyone know how to prove these? (Function & Limits) #2

[harieche]

Hello everyone,

I have been doing a past paper and there are some questions that I cannot prove. Can anyone help me please?

Here is my question:
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2. Prove by the definition that the function : g(x) = -√x+0.5 , (is continuous at the point x=3.)

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[ksdhart2]

Well, since you've not shown any work, I'm forced to assume you're stuck at the very beginning. So, let's begin with the definition of continuity. A function, in this case, g(x), is continuous if, and only if:

\(\displaystyle \displaystyle \lim _{x\to c} g\left(x\right)=g\left(c\right)\)

This statement is, of course, contingent on both the limit and the function evaluated at the specific point existing. So, does the limit of g(x) as x approaches 3 exist? If it does, what is its value? Does g(x) exist at the point x=3? If it does, what is it value? Are the values of the limit and g(3) equal? What can you conclude about whether g(x) is continuous at x=3 or not?