Question
2.1 Introduction to Part 1 of 3 Evaluate the function \( f(r)=\sqrt{r+4}+3 \) at the given values of the independent variable and simplify. a. \( f(-4) \) b. \( f(12) \) c. \( f(x-4) \) a. \( f(-4)= \) \( \square \) (Simplify your answer.)
Ask by Stewart Olson. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. \( f(-4) = 3 \)
b. \( f(12) = 7 \)
c. \( f(x-4) = \sqrt{x} + 3 \)
Solution
Substitute \( r=-4 \) into the expression \( \sqrt{r+4}+3 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\sqrt{r+4}+3\)
- step1: Substitute:
\(\sqrt{-4+4}+3\)
- step2: Add the numbers:
\(\sqrt{0}+3\)
- step3: Simplify the root:
\(0+3\)
- step4: Remove 0:
\(3\)
Substitute \( r=12 \) into the expression \( \sqrt{r+4}+3 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\sqrt{r+4}+3\)
- step1: Substitute:
\(\sqrt{12+4}+3\)
- step2: Add the numbers:
\(\sqrt{16}+3\)
- step3: Simplify the root:
\(4+3\)
- step4: Add the numbers:
\(7\)
Substitute \( r=x-4 \) into the expression \( \sqrt{r+4}+3 \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\sqrt{r+4}+3\)
- step1: Substitute:
\(\sqrt{x-4+4}+3\)
- step2: Remove the opposites:
\(\sqrt{x}+3\)
a. \( f(-4) = 3 \)
b. \( f(12) = 7 \)
c. \( f(x-4) = \sqrt{x} + 3 \)
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To evaluate the function \( f(r)=\sqrt{r+4}+3 \): a. First, substituting \( -4 \) into the function: \[ f(-4) = \sqrt{-4 + 4} + 3 = \sqrt{0} + 3 = 0 + 3 = 3. \] Thus, \( f(-4) = 3 \). b. Now, substituting \( 12 \) into the function: \[ f(12) = \sqrt{12 + 4} + 3 = \sqrt{16} + 3 = 4 + 3 = 7. \] So, \( f(12) = 7 \). c. For \( f(x-4) \): \[ f(x-4) = \sqrt{(x - 4) + 4} + 3 = \sqrt{x} + 3. \] Hence, \( f(x-4) = \sqrt{x} + 3 \). In summary: a. \( f(-4) = 3 \) b. \( f(12) = 7 \) c. \( f(x-4) = \sqrt{x} + 3 \)
