Read the information given below and answer the questions that follow :
If `f(x) = 2x+3 and g(x) =(x-3)/(2)`, then `fog (x)=`

Options

A. 1
B. gof(x)
C. `(15x+9)/(16x-5)`
D. `(1)/(x)`

Answer

To find \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \).

Given:
- \( f(x) = 2x + 3 \)
- \( g(x) = \frac{x - 3}{2} \)

### Step 1: Substitute \( g(x) \) into \( f(x) \)

We need to find \( f(g(x)) \), which means we replace \( x \) in \( f(x) \) with \( g(x) \):

\[ f(g(x)) = f\left(\frac{x - 3}{2}\right) \]

### Step 2: Write the expression for \( f \)

Now, we will use the definition of \( f(x) \):

\[ f(g(x)) = 2\left(\frac{x - 3}{2}\right) + 3 \]

### Step 3: Simplify the expression

Now, we will simplify the expression:

1. Multiply \( 2 \) with \( \frac{x - 3}{2} \):

\[ = \frac{2(x - 3)}{2} + 3 \]

This simplifies to:

\[ = x - 3 + 3 \]

2. Combine like terms:

\[ = x \]

### Final Answer

Thus, \( f(g(x)) = x \).

---