Let `f(x) = ([x]+1)/({x}+1) ` for `f: [0, (5)/(2) ) to ((1)/(2) , 3]`, where `[*]` represents the greatest integer function and `{*}` represents the fractional part of x.
Draw the graph of `y= f(x)`. Prove that `y=f(x)` is bijective. Also find the range of the function.

Explanation

To solve the problem, we will analyze the function \( f(x) = \frac{[x] + 1}{\{x\} + 1} \) defined on the interval \( [0, \frac{5}{2}) \) and find its graph, prove that it is bijective, and determine its range.

### Step 1: Understanding the components of the function
The function involves two parts:
- The greatest integer function \( [x] \), which gives the largest integer less than or equal to \( x \).
- The fractional part function \( \{x\} = x - [x] \), which gives the non-integer part of \( x \).

### Step 2: Determine the behavior of \( f(x) \) in different intervals
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