If a function `f:QtoR` is defined by `f(x)=(2x-1)/(2)` and function `g:QtoR` is defined by `g(x)=(2x-1)/(2)`, then `(gof)((3)/(2))` is

Options

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

Answer

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

### Step 1: Evaluate \( f\left(\frac{3}{2}\right) \)

The function \( f \) is defined as:
\[ f(x) = \frac{2x - 1}{2} \]
Now, substitute \( x = \frac{3}{2} \):
\[ f\left(\frac{3}{2}\right) = \frac{2\left(\frac{3}{2}\right) - 1}{2} \]

### Step 2: Simplify the expression

Calculating the numerator:
\[ 2 \cdot \frac{3}{2} = 3 \]
So we have:
\[ f\left(\frac{3}{2}\right) = \frac{3 - 1}{2} = \frac{2}{2} = 1 \]

### Step 3: Evaluate \( g(1) \)

Next, we need to evaluate \( g(1) \) using the function \( g \), which is defined as:
\[ g(x) = \frac{2x - 1}{2} \]
Now substitute \( x = 1 \):
\[ g(1) = \frac{2(1) - 1}{2} \]

### Step 4: Simplify the expression

Calculating the numerator:
\[ 2 \cdot 1 = 2 \]
So we have:
\[ g(1) = \frac{2 - 1}{2} = \frac{1}{2} \]

### Final Result

Thus, the value of \( (g \circ f)\left(\frac{3}{2}\right) \) is:
\[ \frac{1}{2} \]