Chapter 14: Q. 15 (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 continuous

Step by step solution

Step1. 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 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

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

$f (- 2) = \underset{x \to - 2}{f (x)}$

so the given function is continuous at x =-2

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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

Step1. Given information

Step2. Calculations of continuity

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

Short Answer

Step by step solution

Step1. Given information

Step2. Calculations of continuity

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.

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