Chapter 1: Q. 45 (page 121)

Use graphs to determine if each function is continuous at the given point x = c.
$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 2$

Short Answer

Expert verified

The function is not continuous at x = 2.

Step by step solution

Step 1. Given information.

We have been given a function as:

$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 2$

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

Step 2. Draw the graph.

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, $lim_{x \to 2} f (x) = 0$

For the irrational values of x, $lim_{x \to 2} f (x) = 4$

These two values are different.

Therefore, this function is not continuous at x = 2.

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Use graphs to determine if each function is continuous at the given point x = c.
$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 2$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Draw the graph.

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

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Use graphs to determine if each function is continuous at the given point x = c.f(x)=2−x,ifxrationalx2,ifxirrational,c=2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Draw the graph.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Logic and Functions

Calculus

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use graphs to determine if each function is continuous at the given point x = c.
$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 2$