Chapter 14: Q. 14 (page 905)

In Problem, determine whether f is continuous at c.
$f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x \neq - 2 \\ 4, x = - 2 \end{cases}, c = - 2$

Short Answer

Expert verified

The given polynomial function $f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x \neq - 2 \\ 4, x = - 2 \end{cases}, c = - 2$
is not continuous

Step by step solution

Step.1 Given information

Polynomial function $f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x \neq - 2 \\ 4, x = - 2 \end{cases}, c = - 2$

c=-2

We know that

A function is called continuous function when at x= a,

$\underset{x \to a}{l i m} f (x) = f (a)$

and defined for every number of domain

and $\underset{x \to c}{f (x}) = A a n d f (c) = A$

Step2. Calculations of checking of continuity

Assume that x=-2 is in the domain of the given function, so we can proceed to find the continuity, for continuity x is the approach to -2,

so according to question

$f (x) = \frac{x^{2} - 4}{x + 2} f (x) = \frac{(x + 2) (x - 2)}{(x + 2)} f (x) = x - 2 \underset{x \to - 2}{f (x)} = - 2 - 2 = - 4$

but in question f(-2)= 4

so, $\underset{x \to c}{f (x) \neq} f (c)$ , the function is not continuous

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In Problem, determine whether f is continuous at c.
$f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x \neq - 2 \\ 4, x = - 2 \end{cases}, c = - 2$

Short Answer

Step by step solution

Step.1 Given information

Step2. Calculations of checking of continuity

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In Problem, determine whether f is continuous at c.fx=x2-4x+2,x≠-24,x=-2,c=-2

Short Answer

Step by step solution

Step.1 Given information

Step2. Calculations of checking of continuity

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Applied Mathematics

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Study anywhere. Anytime. Across all devices.

In Problem, determine whether f is continuous at c.
$f (x) = \{\begin{cases} \frac{x^{2} - 4}{x + 2}, x \neq - 2 \\ 4, x = - 2 \end{cases}, c = - 2$