Verified answer

f(x) = (x-2) /(x^2-3x+2)

f(x) = (x-2) /((x-2)(x-1))

This is removable discontinuity

f(x) = 1/(x-1)

when x=2, f(x) = 1/(2-1) = 1

f(x) = 2 when x=1

The value of f(2) that will make f continuous at 2 is 1

Because f(x) = 1/(x -1) for all values other than x = 2 and x = 1, you should assign f(2) = 1/(2 - 1) = 1.