Question

5, 3.1.24 f(x) = 3x² + 5; find f(x + 3) - [f(x) + 3]

Answer 1

Given that $f(x) = 3x^2 + 5$, we have

$f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32$

so that

$f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}$