If `f(x)=2x-3,` find `f(0),f(1),f(-2)andf((x+3)/(2))`.

Answer

To solve the problem, we need to evaluate the function \( f(x) = 2x - 3 \) for the given values: \( f(0) \), \( f(1) \), \( f(-2) \), and \( f\left(\frac{x+3}{2}\right) \).

### Step-by-Step Solution:

1. **Calculate \( f(0) \)**:
\[ f(0) = 2(0) - 3 = 0 - 3 = -3 \]

2. **Calculate \( f(1) \)**:
\[ f(1) = 2(1) - 3 = 2 - 3 = -1 \]

3. **Calculate \( f(-2) \)**:
\[ f(-2) = 2(-2) - 3 = -4 - 3 = -7 \]

4. **Calculate \( f\left(\frac{x+3}{2}\right) \)**:
\[ f\left(\frac{x+3}{2}\right) = 2\left(\frac{x+3}{2}\right) - 3 \]
Simplifying this:
\[ = \frac{2(x+3)}{2} - 3 = x + 3 - 3 = x \]

### Final Results:
- \( f(0) = -3 \)
- \( f(1) = -1 \)
- \( f(-2) = -7 \)
- \( f\left(\frac{x+3}{2}\right) = x \)