Detailed steps of matching method and undetermined coefficient method (undetermined coefficient method should have examples) Given the function f (x-1) = x ^ 2-3x + 2, find f (x + 1) Please use the matching method to list the detailed steps, because I don't know how 2 - (x-1) in step f (x + 1) ^ 2 - (x-1) comes from There are also the detailed steps of undetermined coefficient method (please work out an example for me) It's really troublesome. But thank you for 80

Detailed steps of matching method and undetermined coefficient method (undetermined coefficient method should have examples) Given the function f (x-1) = x ^ 2-3x + 2, find f (x + 1) Please use the matching method to list the detailed steps, because I don't know how 2 - (x-1) in step f (x + 1) ^ 2 - (x-1) comes from There are also the detailed steps of undetermined coefficient method (please work out an example for me) It's really troublesome. But thank you for 80

The known function f (x-1) = x ^ 2-3x + 2
F (x-1) = (x ^ 2-2x + 1) - x + 1 = (x-1) ^ 2 - (x-1) (this 2 is square)
So, let X-1 = a, then f (a) = a ^ 2-a
Then we can substitute a = x + 1
f（x+1）=x^2+x
Undetermined coefficient method
Let f (x-1) = a (x-1) ^ 2 + B (x-1) + C
Expansion: F (x-1) = ax ^ 2 - (2a-b) x + A-B + C
Compared with the formula F (x-1) = x ^ 2-3x + 2
The results show that a = 1, 2a-b = 3, A-B + C = 2
a=1 b=-1 c=0
So, f (x-1) = (x-1) ^ 2 - (x-1)
Same as above