What is the domain of the function f(x) = square root of (12x-24)
I don't get this concept and I have a ton of these problems-can you please explain how to get it
Thank you
What is true of a square root? You cannot take the square root of a negative number (if you're dealing with real numbers anyway). So for what value of X would 12x-24 be 0? anything below that number would make 12x-24 negative and therefore not in the domain.
To find the domain of a function, we need to determine the set of all possible values for which the function is defined. In this case, we have the function f(x) = √(12x - 24).
To find the domain, we need to consider any restrictions on the input variable x.
In this case, the only potential restriction is the square root function itself. The square root function is defined only for non-negative real numbers. Therefore, the expression inside the square root, 12x - 24, must be greater than or equal to 0.
To solve this inequality, we set 12x - 24 greater than or equal to 0 and solve for x:
12x - 24 ≥ 0
Adding 24 to both sides, we have:
12x ≥ 24
Dividing both sides by 12, we get:
x ≥ 2
Therefore, the domain of the function is all real numbers greater than or equal to 2. In interval notation, it can be expressed as [2, ∞).
In summary, to find the domain of a function, you need to identify any restrictions on the input variable and solve any inequalities accordingly. For the given function f(x) = √(12x - 24), the domain is x ≥ 2.