Evaluate and simplify

F (x) = 3-6x^2 for f (x+3)

Insert x + 3 instead of x into the equation of the function f (x):

f (x) = 3 - 6x²

f (x + 3) = 3 - 6 (x + 3) ²

use (a + b) ² = a² + 2ab + b²

= 3 - 6 (x² + 2 (x) (3) + 3²) = 3 - 6 (x² + 6x + 9)

use distributive property

= 3 + (-6) (x²) + (-6) (6x) + (-6) (9) = 3 - 6x² - 36x - 54

combine like terms

= - 6x² - 36x - 51

Answer: f (x + 3) = - 6x² - 36x - 51