For what value of c is the function f(x) continuous at x = -4?

Question

For what value of c is the function continuous at x = - 4

f(x)= c when x = -4

4 when x = 1

(x^2-16)/(x+4)(x-6) otherwise

Answer 1

f(x) = (x² - 16)/(x + 4)(x - 6) if x ≠ - 4 and x ≠ 1

f(- 4) = c and f(1) = 4.

f(x) = (x- 4)(x + 4)/(x + 4)(x - 6) = (x - 4)/(x - 6) if x ≠ -4;

limf(x) = (-4 - 4)/(-4 - 6) = 4/5; f(c) = 4/5

x → - 4