Let `f:N rarr R` be the function defined by `f(x)=(2x-1)/2` and `g:Q rarr Q` be another function defined by `g(x)=x+2` then `(gof)(3/2)` is

Options

A. 1
B. 1
C. `(7)/(2)`
D. None of these

Explanation

To solve the problem, we need to find \((g \circ f)(\frac{3}{2})\), which means we first apply the function \(f\) to \(\frac{3}{2}\), and then apply the function \(g\) to the result of \(f\).

### Step-by-Step Solution:

1. **Define the Functions**:
- The function \(f\) is defined as:
\[ f(x) = \frac{2x - 1}{2} \]
- The function \(g\) is defined as:
\[ g(x) = x + 2 \]

2. **Calculate \(f\left(\frac{3}{2}\right)\)**:
- Substitute \(\frac{3}{2}\) into the function \(f\):
\[ f\left(\frac{3}{2}\right) = \frac{2 \cdot \frac{3}{2} - 1}{2} \]
- Simplify the expression:
\[ = \frac{3 - 1}{2} = \frac{2}{2} = 1 \]

3. **Calculate \(g(f(\frac{3}{2}))\)**:
- Now we need to find \(g(1)\):
\[ g(1) = 1 + 2 = 3 \]

4. **Final Result**:
- Therefore, \((g \circ f)\left(\frac{3}{2}\right) = g(f(\frac{3}{2})) = g(1) = 3\).

### Conclusion:
The final answer is:
\[ (g \circ f)\left(\frac{3}{2}\right) = 3 \]