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Chapter 1: Problem 23

Find the \(x\) -values (if any) at which \(f\) is not continuous. Which of the discontinuities are removable? $$ f(x)=x^{2}-2 x+1 $$

Short Answer

Expert verified
The function \(f(x) = x^2 -2x +1\) has no discontinuities and hence no removable discontinuities.

Step by step solution

01

Confirm the given function

The given function is \(f(x) = x^2 -2x +1\). It's a polynomial function, thus it's continuous everywhere.
02

Identifying the denominators

In the expression of \(f(x)\), there is no denominator that involves the term \(x\), therefore the function does not have any values of \(x\) at which it is undefined or discontinuous.
03

Check for removable discontinuity

A function has a removable discontinuity at a point if there is a hole at that point. However, as this function is continuous for all values of \(x\), it doesn't have any holes or jumps in its graph that might suggest a discontinuity.

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