For what value of b is f continuous at x=2?

Question

f(x)= x² - 3bx + 2 ; x ≤ 2

2bx² - 8 ; x > 2

Answer 1

limf(x) x →2^- = limf(x) x→2⁺ = f(2);

limf(x) x →2^- = lim(x² - 3bx + 2) x →2 = 4 - 6b + 2 = 6 - 6b

limf(x) x →2⁺ = lim(2bx² - 8) x →2 = 2b·4 - 8 = 8b - 8; f(2) = 4 - 6b + 2 = 6 - 6b;

6 - 6b = = 8b - 8; 14b [= 14 b = 1.

Answer: for f(x) to be continues at x = 2 b must be equel 1.