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

Options

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

Answer

To solve the problem, we need to find the value of \((g \circ f)\left(\frac{3}{2}\right)\). This means we first need to evaluate \(f\left(\frac{3}{2}\right)\) and then use that result to evaluate \(g\) at that value.

### Step-by-step Solution:

1. **Identify 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. **Evaluate \(f\left(\frac{3}{2}\right)\):**
- 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. **Now evaluate \(g(f\left(\frac{3}{2}\right))\):**
- We found that \(f\left(\frac{3}{2}\right) = 1\), so we need to evaluate \(g(1)\):
\[ g(1) = 1 + 2 = 3 \]

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

### Conclusion:
The value of \((g \circ f)\left(\frac{3}{2}\right)\) is \(3\).