Question 991885
f(x) = 4x^2 - 3x + 7


f(k-1) = 4(k-1)^2 - 3(k-1) + 7


you just replace x with (k-1).


the rest is just simplification.


(k-1)^2 = k^2 - 2k + 1


the equation becomes:


f(k-1) = 4(k^2 - 2k + 1) - 3(k-1) + 7


simplify to get:


f(k-1) = 4k^2 - 8k + 4 - 3k + 3 + 7


combine like terms to get:


f(k-1) = 4k^2 - 11k + 14.


that's your solution.


i verified that's it's true.
i did it by making x = 5 and then evaluating the original equation.
i then made k = 6 and evaluated the final equation.
the answers were the same which confirms the solution is correct.