5. Given the function (cxl, x < 2
f(x) =
CX - 3, x > 2
Determine the value of c so that the function will be continuous everywhere.

I need #5 with an explanation please

The function

is piecewise continuous, since both cx ² and cx - 3 are polynomials. f(x) itself is continuous if both pieces meet at the same defined point. In other words, the limits of f(x) as x → 2 from either side have the same value of f (2) = c•2² = 4c.

We have

so in order for f to be continuous, we need

4c = 2c - 3   →   2c = -3   →   c = -3/2