1. ## Extended function

Let F(x) = [(x² + 3x -4) / (x² - 4x + 3)]

Give a formula for the extended function that is continuous at x=1

2. Originally Posted by h4hv4hd4si4n
Let F(x) = [(x² + 3x -4) / (x² - 4x + 3)]

Give a formula for the extended function that is continuous at x=1
Notice that

$\frac{x^2 + 3x -4}{x^2 - 4x + 3} = \frac{(x+4)(x-1)}{(x-3)(x-1)}$

so the terms $(x-1)$ will cancel provided that $x \ne 1$

So let us define the extended function $G(x)$ such that

$G(x) = \left\{\begin{array}{cc}\frac{x+4}{x-3},&\mbox{ if }
x \ne 1\\- \frac{5}{2}, & \mbox{ if } x=1.\end{array}\right.$

3. thanks so much!

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# define extended function

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