If you are given the radical expression,√𝑥 − 4, what is the restriction on the value of x? Explain.
The restriction on the value of x is that it must be greater than or equal to 4.
This is because the expression √𝑥 − 4 represents the square root of x minus 4. The square root can only be defined for non-negative real numbers.
If x is less than 4, then √𝑥 − 4 would result in a negative value under the square root, which is not a real number. Therefore, the value of x must be greater than or equal to 4 for the radical expression to be defined.
The restriction on the value of x in the radical expression √x - 4 depends on the domain of the square root function.
The square root function, √x, is only defined for non-negative values of x. This means that the value inside the square root, x, must be greater than or equal to zero. If x is negative, the square root function does not have a real solution.
In the given expression √x - 4, we have the square root function with x as its argument. In order for this expression to have a real solution, the value inside the square root (x) must be greater than or equal to zero.
Therefore, the restriction on the value of x is x ≥ 0. This means that x cannot be negative, and it must be equal to or greater than zero for the given radical expression to have a real solution.
To find the restriction on the value of x for the given radical expression √𝑥 − 4, we need to consider the domain of the square root function.
The square root function, denoted as √𝑥, is defined only for non-negative real numbers. In other words, you cannot take the square root of a negative number and expect a real number solution.
In our expression, √𝑥 − 4, the square root is applied to 𝑥 first, and then the result is subtracted by 4. Therefore, to ensure the square root function is defined, the expression within the square root (√𝑥) must be greater than or equal to zero.
Mathematically, we can write this as:
𝑥 - 4 ≥ 0
Solving this inequality, we find:
𝑥 ≥ 4
Hence, the restriction on the value of x for the given radical expression √𝑥 − 4 is 𝑥 ≥ 4, meaning that 𝑥 must be equal to or greater than 4.