Domain and Range: Radical: For, find the domain and range.

Domain:  The quantity is defined for all x. Since we can take the square root of a quantity only if the quantity is 0 or positive, we must require (36 - x²) to be greater than or equal to zero:

.

By the addition rule for inequalities, we can add -36 to each side to get

.

By the negative multiplication rule for inequalities, we can multiply both sides by -1 and change the direction of the inequality to get

x² £ 36.

We see that we have two possibilities for the domain:

x £ 6 and x ³ -6.

Range: Now that the quantity (36 - x²) is constrained to be positive or zero, f(x) will also be constrained to be positive or zero. Hence the range is .