   Chapter 1.6, Problem 26E

Chapter
Section
Textbook Problem

Determining Continuity In Exercises 11-40, describe the interval(s) on which the function is continuous. Explain why the function is continuous on the interval(s). If the function has a discontinuity, identify the conditions of continuity that are not satisfied. See Examples 1, 2, 3, 4, and 5. f ( x ) = 3 − x

To determine

To calculate: The interval(s) on which the function f(x)=3x is continuous and estimate the conditions that are not satisfied, if the function f(x)=3x has any discontinuity.

Explanation

Given Information:

The provided function is f(x)=3x.

Formula used:

The function f is continuous at c when these three properties satisfies:

f(c) is defined.

limxcf(x) exists.

limxcf(x)=f(c)

Calculation:

Consider the provided function, f(x)=3x

To check the continuity of function,

The function f(x)=3x is defined only when the values inside the square-root is positive.

That is,

x0

Also, the maximum value of the real number is and any expression is not defined at point . So, the domain of this function is the interval [0,).

Substitute 0 for x in the provided function.

f(0)=30=3

Therefore, the function exists at point 0.

To check the limit of function,

limx0f(x)=limx0(3x)=30=3

Now, from the above calculation limx0f(x)=f(0).

The provided function satisfies all the condition for x0

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