Exercises 5–10 refer to the function graphed

Chapter 2, Problem 10E

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QUESTION:

Exercises 5–10 refer to the function

 

            \(f(x)=\left\{\begin{array}{lrl}x^{2}-1, & -1 \leq x<0 \\2 x, & 0<x<1 \\1, & x=1 \\-2 x+4, & 1<x<2 \\0, &2<x<3\end{array}\right.\)

graphed in the accompanying figure.

                                         

To what new value should \(f(1)\)  be changed to remove the discontinuity?

Equation  Transcription:

{

Text Transcription:

f(x)={_0,  2 < x < 3 ^-2x + 4,1 < x < 2  ^1, x = 1 ^2x,  0 < x < 1 ^x^2-1,  -1 leq x < 0

f(1)

Questions & Answers

QUESTION:

Exercises 5–10 refer to the function

 

            \(f(x)=\left\{\begin{array}{lrl}x^{2}-1, & -1 \leq x<0 \\2 x, & 0<x<1 \\1, & x=1 \\-2 x+4, & 1<x<2 \\0, &2<x<3\end{array}\right.\)

graphed in the accompanying figure.

                                         

To what new value should \(f(1)\)  be changed to remove the discontinuity?

Equation  Transcription:

{

Text Transcription:

f(x)={_0,  2 < x < 3 ^-2x + 4,1 < x < 2  ^1, x = 1 ^2x,  0 < x < 1 ^x^2-1,  -1 leq x < 0

f(1)

ANSWER:

Solution:

Step 1 of 2:

In this problem, we need to find the new value of  that should be changed to remove the discontinuity.

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