Chapter 1: Q. 19 (page 135)

Graph the functions $f (x) = x + 1$ and $g (x) = \frac{x^{2} - 1}{x - 1}$ , and show that they are equal everywhere except at one point. Then show that f(x) and g(x) have different values, but the same limit, at this point.

Short Answer

Expert verified

Both functions approach 2 when x approaches 1.

Step by step solution

Step 1. Given information.

Given functions are:

$f (x) = x + 1 g (x) = \frac{x^{2} - 1}{x - 1}$

We have to graph the function.

Step 2. Graph the f(x)

Graph of $f (x) = x + 1$ is:

Step 3. Graph the g(x)

Graph of $g (x) = \frac{x^{2} - 1}{x - 1}$ is:

Step 4. Compare the graphs.

The graph of g looks similar to the graph of f but with the hole at $x = 1$

Here,

$f (1) = 2$ but $g (1)$ is undefined.

and both functions approach 2 when x approaches 1.

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Graph the functions $f (x) = x + 1$ and $g (x) = \frac{x^{2} - 1}{x - 1}$ , and show that they are equal everywhere except at one point. Then show that f(x) and g(x) have different values, but the same limit, at this point.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the f(x)

Step 3. Graph the g(x)

Step 4. Compare the graphs.

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Graph the functions f(x)=x+1 and g(x)=x2−1x−1, and show that they are equal everywhere except at one point. Then show that f(x) and g(x) have different values, but the same limit, at this point.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Graph the f(x)

Step 3. Graph the g(x)

Step 4. Compare the graphs.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

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Study anywhere. Anytime. Across all devices.

Graph the functions $f (x) = x + 1$ and $g (x) = \frac{x^{2} - 1}{x - 1}$ , and show that they are equal everywhere except at one point. Then show that f(x) and g(x) have different values, but the same limit, at this point.