Question

If f(×) = ac{1}{ \sqrt{x - 1} } " alt=" \frac{1}{ \sqrt{x - 1} } " align="absmiddle" class="latex-formula">
then find $\frac{f(x) - f(2)}{x - 2}$
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Answer 1

9514 1404 393

Answer:

  (1 -x +√(x -1))/(x² -3x +2)

Step-by-step explanation:

Fill in the given function definition and simplify.

  $\dfrac{f(x)-f(2)}{x-2}=\dfrac{\dfrac{1}{\sqrt{x-1}}-\dfrac{1}{\sqrt{2-1}}}{x-2}=\dfrac{1-\sqrt{x-1}}{(x-2)\sqrt{x-1}}\\\\=\dfrac{\sqrt{x-1}-x+1}{(x-2)(x-1)}=\boxed{\dfrac{\sqrt{x-1}-x+1}{x^2-3x+2}}$