Final answer:
To make the function continuous everywhere, we need to find the value of c for which both pieces of the function meet at their common point.
Step-by-step explanation:
For the function f(x) = { x^2 - 3, x ≤ c, 4x - 7, x > c } to be continuous everywhere, the two pieces of the function must meet at their common point. In other words, the value of the function at x = c must be equal for both pieces.
So, we need to find the value of c for which c^2 - 3 = 4c - 7. Solving this equation, we get c = 4 or c = -2.
Therefore, the value of c that makes the function continuous everywhere is c = 4.