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Problem 1

# Complete the given sentence. The closed-form function $$f(x)=\frac{1}{x-1}$$ is continuous for all $$x$$ except HINT [See Quick Example on page 707.]

Expert verified
The closed-form function $$f(x)=\frac{1}{x-1}$$ is continuous for all $$x$$ except $$x = 1$$.
See the step by step solution

## Step 1: Identify the denominator

In this function, the denominator is $$x-1$$.

## Step 2: Find the value of x that makes the denominator equal to zero

To find the value of x when the denominator is equal to zero, set the denominator equal to zero and solve for x: $$x - 1 = 0$$

## Step 3: Solve the equation

Add 1 to both sides of the equation: $$x = 1$$ The closed-form function $$f(x)=\frac{1}{x-1}$$ is continuous for all $$x$$ except $$x = 1$$.

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