Determine a value c so that f is continuous.

Question

f(x)={x+3 x≤2}

{cx+6 x>2}

Answer 1

Hi, Connor.

For f to be continuous, in particular it must be continuous at x = 2. So the left- and right-hand limits of f(x) as x -> 2 must be equal to f(2). By definition of f, f(2) = 2 + 3 = 5. The right-hand limit lim(x -> 2+) f(x) = lim(x -> 2+) (cx + 6) = 2c + 6. Thus 5 = 2c + 6, or c = -1/2.