If f(×) = (1)/( √(x - 1) ) then find (f(x) - f(2))/(x - 2) ​

Question

If f(×) =
`(1)/( √(x - 1) )`

then find
`(f(x) - f(2))/(x - 2)`
​

Answer 1

9514 1404 393

Answer:

(1 -x +√(x -1))/(x² -3x +2)

Explanation:

Fill in the given function definition and simplify.

`(f(x)-f(2))/(x-2)=((1)/(√(x-1))-(1)/(√(2-1)))/(x-2)=(1-√(x-1))/((x-2)√(x-1))\\\\=(√(x-1)-x+1)/((x-2)(x-1))=\boxed{(√(x-1)-x+1)/(x^2-3x+2)}`