Question

To the function attached,Is f(x) continuous at x=1? Please explain

Answer 1

Recall that a function is continuous at a point if the limit as the variable approaches a value is the same as the value of the function at that point.

Now, notice that, using the definition of the function:

`\begin{gathered} \lim_(x\to1^+)f(x)=√(1)+2=3, \\ \lim_(x\to1^-)f(x)=3, \end{gathered}`

therefore:

`\lim_(x\to1)f(x)=3.`

Given that the limit and the value of the function at x=1 are equal, the function is continuous at x=1.

Answer: It is continuous at x=1.