f(x-1)=x2+3x+2 then f(x-2) =?

f(x-1)=x²+3x+2. then f(x-2) =?

Dear student

f (x - 1) = x^{2} + 3 x + 2 = x^{2} + 2 x + x + 2 = x (x + 2) + 1 (x + 2) = (x + 1) (x + 2) s o, f (x - 1) = (x + 1) (x + 2) r e p l a c i n g x b y x + 1, w e g e t f (x + 1 - 1) = (x + 1 + 1) (x + 1 + 2) f (x) = (x + 2) (x + 3) t o g e t f (x - 2), w e r e p l a c e x b y x - 2 f (x - 2) = (x - 2 + 2) (x - 2 + 3) = x (x + 1) = x^{2} + x

Regards