If f(x)`=x^(2)andg(x)=2x+1 ` are two real valued function, then evaluate :
`(f+g)(x),(f-g)(x),(fg)(x),(f)/(g)(x)`

Explanation

To solve the problem, we need to evaluate the following expressions based on the given functions \( f(x) = x^2 \) and \( g(x) = 2x + 1 \):

1. \( (f + g)(x) \)
2. \( (f - g)(x) \)
3. \( (fg)(x) \)
4. \( \frac{f}{g}(x) \)

Let's go through each step:

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

To find \( (f + g)(x) \), we add the two functions:

\[ (f + g)(x) = f(x) + g(x) \]

Substituting the given functions:

\[ = x^2 + (2x + 1) \]

Now, combine like terms:

\[ = x^2 + 2x + 1 \]

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

To find \( (f - g)(x) \), we subtract \( g(x) \) from \( f(x) \):

\[ (f - g)(x) = f(x) - g(x) \]

Substituting the given functions:

\[ = x^2 - (2x + 1) \]

Distributing the negative sign:

\[ = x^2 - 2x - 1 \]

### Step 3: Evaluate \( (fg)(x) \)

To find \( (fg)(x) \), we multiply the two functions:

\[ (fg)(x) = f(x) \cdot g(x) \]

Substituting the given functions:

\[ = x^2 \cdot (2x + 1) \]

Distributing \( x^2 \):

\[ = 2x^3 + x^2 \]

### Step 4: Evaluate \( \frac{f}{g}(x) \)

To find \( \frac{f}{g}(x) \), we divide \( f(x) \) by \( g(x) \):

\[ \frac{f}{g}(x) = \frac{f(x)}{g(x)} \]

Substituting the given functions:

\[ = \frac{x^2}{2x + 1} \]

### Final Answers

1. \( (f + g)(x) = x^2 + 2x + 1 \)
2. \( (f - g)(x) = x^2 - 2x - 1 \)
3. \( (fg)(x) = 2x^3 + x^2 \)
4. \( \frac{f}{g}(x) = \frac{x^2}{2x + 1} \)