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

 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 (3x - 4) to be greater than or equal to zero:

.

By the addition rule for inequalities, we can add 4 to each side to get

.

By the multiplication rule for inequalities, we can multiply both sides by 1/3 to get

. Hence this is the domain of f(x).

Range: Now that the quantity (3x - 4) is constrained to be positive or zero, f(x) will also be constrained to be positive or zero. Hence the range is .