Finding f (x) by knowing that the function is a linear function and satisfies the relation 3f (x + 1) - 2F (x-1) = 2x-17

Finding f (x) by knowing that the function is a linear function and satisfies the relation 3f (x + 1) - 2F (x-1) = 2x-17

Using undetermined coefficient method
Since f (x) is a linear function, Let f (x) = KX + B
Ψ f (x + 1) = K (x + 1) + B = KX + K + B (where x is replaced by X + 1)
Ψ f (x-1) = K (x-1) + B = kx-k + B (where x is replaced by x-1)
∵3f(x+1)-2f(x-1)=2x+17
∴3kx+3k+3b-2kx+2k-2b=2x+17
∴kx+(5k+b)=2x+17
| k = 2,5k + B = 17 (the coefficients of corresponding terms are equal)
∴k=2,b=7
∴f(x)=2x+7