Question

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

Answer 1

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