Math Problem Statement

Evaluate the function f left parenthesis r right parenthesis equals StartRoot r plus 7 EndRoot plus 9 at the given values of the independent variable and simplify. a.  f left parenthesis negative 7 right parenthesis      b.  f left parenthesis 9 right parenthesis      c.  f left parenthesis x minus 7 right parenthesis Question content area bottom Part 1 a.  f left parenthesis negative 7 right parenthesisequals    enter your response here ​(Simplify your​ answer.)

Solution

We are given the function:

f(r)=r+7+9f(r) = \sqrt{r + 7} + 9

We need to evaluate this function at the given values of the independent variable.

a. f(−7)f(-7)

Substitute r=−7r = -7 into the function:

f(−7)=−7+7+9=0+9=0+9=9f(-7) = \sqrt{-7 + 7} + 9 = \sqrt{0} + 9 = 0 + 9 = 9

Thus, f(−7)=9f(-7) = 9.

Would you like to continue with parts b and c, or need further clarification on part a?

Here are 5 relative questions:

  1. How does changing the constant inside the square root affect the function?
  2. What happens if r=−8r = -8 instead of r=−7r = -7?
  3. How would the function change if the square root was squared?
  4. Can you graph f(r)f(r) for different values of rr?
  5. How does the domain of this function change?

Tip: Always check that the expression inside a square root is non-negative when dealing with real numbers.

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Math Problem Analysis

Mathematical Concepts

Functions
Square Roots
Substitution

Formulas

f(r) = √(r + 7) + 9

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 8-10

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