Let f and g be two real valued functions ,defined by f(x) =x ,g(x)=[x]. Then find the value of `f+g`

Answer

To find the value of \( f + g \) where \( f(x) = x \) and \( g(x) = [x] \) (the greatest integer function), we will follow these steps:

### Step 1: Define the Functions
We have two functions defined as:
- \( f(x) = x \)
- \( g(x) = [x] \) (the greatest integer less than or equal to \( x \))

### Step 2: Write the Expression for \( f + g \)
The expression for \( f + g \) is given by:
\[ f + g = f(x) + g(x) \]

### Step 3: Substitute the Functions into the Expression
Now, substituting the definitions of \( f(x) \) and \( g(x) \) into the expression:
\[ f + g = x + [x] \]

### Step 4: Final Expression
Thus, the value of \( f + g \) is:
\[ f + g = x + [x] \]

### Conclusion
The final answer is:
\[ f + g = x + [x] \]

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