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Chapter 1: Q. 48 (page 121)

Use graphs to determine if each function is continuous at the given point x = c.

f(x)=x2−3,    ifxrational3x+1,    ifxirrational,c=4

Short Answer

Expert verified

The function is continuous at x = 4.

Step by step solution

01

Step 1. Given information.

We have been given a function as:

f(x)=x2−3,    ifxrational3x+1,    ifxirrational,c=4

We have to determine if this function is continuous at the given point x = c.

02

Step 2. Draw the graph.

03

Step 3. Analyze the graph for the continuity of the function at x = c.

From the graph, we can see that:

For the rational values of x,limx→4 f(x)=13

For the irrational values of x, limx→4 f(x)=13

These two values are equal.

Therefore, this function is continuous at x = 4.

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Most popular questions from this chapter

Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.

f is left continuous at x = 2 but not continuous at x = 2, and f(2) = 3.

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