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Chapter 14: Q. 31 (page 889)

In Problems 13鈥�32, use the accompanying graph of y = f(x).

\

Is f continuous at 4?

Short Answer

Expert verified

The answer is no. The function is not continuous at 4.

Step by step solution

01

Step. 1 How to check continuity? 

For a function to be continuous its LHL = RHL = f(c) at the point x=c.

02

Step. 2 Calculating LHL, RHL and f(c). 

As we can see that x=4doesn't exist even in the domain of f(x).

So, f(4) doesn't exist. Therefore, we don't need to calculate LHL and RHL from here itself we can conclude that f(x) is not continuous at x=4.

And from the graph itself we can clearly see that we have to pick our pencil up the paper when we move through x=4which is also a method to check whether the function is continuous or not.

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