If `f(x)=x^(2) and g(x)=2x` , then evaluate,
(i) `(f+g)(3)" "(ii) (f-g)(2)`
(iii) `(f*g)(1)" "(iv) ((f)/(g))(5)`

Answer

To solve the problem, we need to evaluate the following expressions using the given functions \( f(x) = x^2 \) and \( g(x) = 2x \):

1. \( (f + g)(3) \)
2. \( (f - g)(2) \)
3. \( (f \cdot g)(1) \)
4. \( \left( \frac{f}{g} \right)(5) \)

Let's evaluate each one step by step.

### Step 1: Evaluate \( (f + g)(3) \)

**Solution:**
- First, we need to find \( f(3) \) and \( g(3) \).
- \( f(3) = 3^2 = 9 \)
- \( g(3) = 2 \cdot 3 = 6 \)
- Now, we add these two results:
\[ (f + g)(3) = f(3) + g(3) = 9 + 6 = 15 \]

### Step 2: Evaluate \( (f - g)(2) \)

**Solution:**
- Next, we find \( f(2) \) and \( g(2) \).
- \( f(2) = 2^2 = 4 \)
- \( g(2) = 2 \cdot 2 = 4 \)
- Now, we subtract \( g(2) \) from \( f(2) \):
\[ (f - g)(2) = f(2) - g(2) = 4 - 4 = 0 \]

### Step 3: Evaluate \( (f \cdot g)(1) \)

**Solution:**
- We need to find \( f(1) \) and \( g(1) \).
- \( f(1) = 1^2 = 1 \)
- \( g(1) = 2 \cdot 1 = 2 \)
- Now, we multiply these two results:
\[ (f \cdot g)(1) = f(1) \cdot g(1) = 1 \cdot 2 = 2 \]

### Step 4: Evaluate \( \left( \frac{f}{g} \right)(5) \)

**Solution:**
- We find \( f(5) \) and \( g(5) \).
- \( f(5) = 5^2 = 25 \)
- \( g(5) = 2 \cdot 5 = 10 \)
- Now, we divide \( f(5) \) by \( g(5) \):
\[ \left( \frac{f}{g} \right)(5) = \frac{f(5)}{g(5)} = \frac{25}{10} = 2.5 \]

### Final Answers:
1. \( (f + g)(3) = 15 \)
2. \( (f - g)(2) = 0 \)
3. \( (f \cdot g)(1) = 2 \)
4. \( \left( \frac{f}{g} \right)(5) = 2.5 \)