Need help solving a functions problem.?

Question

I have completely forgotten how to find the domain and range of f(x)=square root of (3x+6). If anyone could help, that would be great.

Answer 1

The square root of a number must be greater than or equal to 0.

3x+6 >=0

3x >=-6

x >=-2

Domain [-2, ∞)

Range : [ -∞, ∞] : all real numbers

Answer 2

take the expression under the radical and set it to >=0 (greater than or equal to zero) and then solve for x.

3x+6>=0

3x>=-6

x>=-2

if you write it in interval notation then the solution is [-2,infinity)

Answer 3

f(x) = √(3x+6)

The radicand can't be negative, so

3x+6 ≥ 0

3x ≥ -6

x ≥ -2

f(x) ≥ 0

The domain is {x: x≥2} and the range is {y: y≥0}