Find a, such that the function f(x)=3x+rad(a-x^2) has the domain [-6,6].

To find the value of "a" such that the function has the given domain, we need to determine the range of the expression inside the square root (rad). Since the square root of a negative number is not defined in the real number system, we want to avoid any values of "a-x^2" that would result in a negative number.

First, let's find the minimum and maximum values of "a-x^2" for the given domain [-6, 6].

For the minimum value, we substitute x = -6 into "a-x^2":
a - (-6)^2 = a - 36

For the maximum value, we substitute x = 6 into "a-x^2":
a - (6)^2 = a - 36

Since we want to avoid negative values in the square root, we need to make sure that a - 36 is greater than or equal to zero. This gives us the inequality:

a - 36 ≥ 0

To solve this inequality for a, we add 36 to both sides of the inequality:

a ≥ 36

So, the value of "a" such that the function has the domain [-6,6] is any value greater than or equal to 36.