In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 b. f(10)

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Step 1: Understand the problem. The function f(r) = √(r + 6) + 3 is given, and you are tasked with evaluating it at r = 10. This means substituting 10 for r in the function.

Step 2: Substitute r = 10 into the function. Replace r in the expression √(r + 6) + 3 with 10, resulting in f(10) = √(10 + 6) + 3.

Step 3: Simplify the expression inside the square root. Add 10 and 6 to get 16, so the function becomes f(10) = √(16) + 3.

Step 4: Evaluate the square root. The square root of 16 is 4, so the function simplifies further to f(10) = 4 + 3.

Step 5: Add the remaining terms. Combine 4 and 3 to complete the simplification of f(10).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable in a function. In this case, we replace 'r' in the function f(r) = √(r + 6) + 3 with the value 10. This process allows us to determine the output of the function for that particular input.

Square Root Function

The square root function, denoted as √x, represents the principal square root of x, which is the non-negative value that, when squared, gives x. In the function f(r), the term √(r + 6) requires us to ensure that the expression inside the square root is non-negative, as square roots of negative numbers are not defined in the realm of real numbers.

Simplification

Simplification is the process of reducing an expression to its simplest form. After evaluating the function at a specific value, we may need to combine like terms or perform arithmetic operations to arrive at a final, simplified answer. This step is crucial for clarity and ease of understanding in mathematical expressions.

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