For what value of a is the following function continuous

Question

For what value of a is the following function continuous at every x?

f(x)= a²x+2a, x≥2

24, x<2

Answer 1

The function is clearly continuous for x < 2 and for x > 2.

The only possibility of discontinuity is at x = 2.

To make it continuous requires f(2) = 24.

2a² + 2a = 24

a² + a - 12 = 0

a = (-1 +- sqrt(1 + 48))/2

So the function is continuous for a = 3 and a = -4.