State the restrictions on the variables √𝑥 − 5
The restrictions on the variable √𝑥 − 5 are as follows:
1. The expression under the square root (√𝑥 − 5) must be greater than or equal to zero since imaginary numbers are not allowed. This implies that 𝑥 must be greater than or equal to 25.
Mathematically, it can be written as 𝑥 ≥ 25.
To find the restrictions on the variable 𝑥 in the expression √𝑥 - 5, we need to consider the domain of the square root function and any additional restrictions.
1. Domain of the square root function:
The square root function (√𝑥) is defined only for non-negative values of 𝑥. This means that 𝑥 must be greater than or equal to zero.
2. Additional restrictions:
In the expression √𝑥 - 5, there are no additional restrictions imposed. Therefore, 𝑥 can take any non-negative value (including zero).
To summarize, the restrictions on the variable 𝑥 in the expression √𝑥 - 5 are 𝑥 ≥ 0.
To determine the restrictions on the variable √𝑥 − 5, we need to consider the domain of the square root function (√𝑥). The square root of a number is only defined for non-negative numbers (≥ 0). Therefore, the expression √𝑥 − 5 has restrictions based on the value inside the square root.
For √𝑥 − 5 to be defined, we need √𝑥 to be greater than or equal to 5. This can be represented mathematically as:
√𝑥 ≥ 5
To find 𝑥, we square both sides of the inequality:
(√𝑥)² ≥ 5²
𝑥 ≥ 25
So, the restrictions on the variable √𝑥 − 5 are 𝑥 ≥ 25. In other words, 𝑥 must be greater than or equal to 25 for the expression to be defined.