For r `gt` 0, f(r) is the ratio of perimeter to area of a circle of radius r. Then f(1)+f(2) is equal to

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to find the function \( f(r) \) which represents the ratio of the perimeter to the area of a circle with radius \( r \).

### Step-by-Step Solution:

1. **Identify the formulas for perimeter and area of a circle**:
- The perimeter (circumference) \( C \) of a circle is given by:
\[ C = 2\pi r \]
- The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]

2. **Set up the function \( f(r) \)**:
- The function \( f(r) \) is defined as the ratio of the perimeter to the area:
\[ f(r) = \frac{C}{A} = \frac{2\pi r}{\pi r^2} \]

3. **Simplify the function**:
- Cancel out \( \pi \) from the numerator and denominator:
\[ f(r) = \frac{2r}{r^2} \]
- Further simplify by canceling \( r \) (since \( r > 0 \)):
\[ f(r) = \frac{2}{r} \]

4. **Calculate \( f(1) \)**:
- Substitute \( r = 1 \):
\[ f(1) = \frac{2}{1} = 2 \]

5. **Calculate \( f(2) \)**:
- Substitute \( r = 2 \):
\[ f(2) = \frac{2}{2} = 1 \]

6. **Add \( f(1) \) and \( f(2) \)**:
- Now, we find \( f(1) + f(2) \):
\[ f(1) + f(2) = 2 + 1 = 3 \]

### Final Answer:
Thus, \( f(1) + f(2) = 3 \).

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