Certainly! Let's work through the problem step by step to express the mathematical function:
1. Start with the original expression:
[tex]\[ 10 - \sqrt{x + 3} \][/tex]
2. Identify the components:
- The constant term is [tex]\( 10 \)[/tex].
- There is a square root function, [tex]\(\sqrt{x + 3}\)[/tex], subtracted from the constant term.
3. Understand the square root function:
- The expression inside the square root is [tex]\( x + 3 \)[/tex].
- The square root function, [tex]\(\sqrt{\cdot}\)[/tex], only operates on positive arguments (the square root of a negative number is not defined within the realm of real numbers).
4. Combine everything into the final function:
- When we subtract [tex]\(\sqrt{x + 3}\)[/tex] from 10, the result is:
[tex]\[ 10 - \sqrt{x + 3} \][/tex]
So, the detailed step-by-step process involves recognizing each part of the expression and how they combine to form the final function [tex]\( 10 - \sqrt{x + 3} \)[/tex].
