If function f is defined by f (x) = 3x2 - 5x + 4, what is f (x-4) ?

To find f(x-4), we substitute (x-4) into the function f(x) = 3x^2 - 5x + 4.

Step 1: Substitute (x-4) into the function f(x-4) = 3(x-4)^2 - 5(x-4) + 4

Step 2: Expand the equation = 3(x^2 - 8x + 16) - 5x + 20 + 4

Step 3: Distribute the 3 and -5 across the terms in the parentheses = 3x^2 - 24x + 48 - 5x + 20 + 4

Step 4: Combine like terms = 3x^2 - 29x + 72

So, f(x-4) = 3x^2 - 29x + 72.