If function f is defined by `f(x)=5x+3,` then which expression represent `2f(x)-3`?

Options

A. `10x-3`
B. `10x+3`
C. `10x`
D. `3`

Answer

To solve the question, we need to find the expression for \(2f(x) - 3\) given that \(f(x) = 5x + 3\).

### Step-by-Step Solution:

1. **Identify the function**: We know that \(f(x) = 5x + 3\).

2. **Multiply the function by 2**: We need to calculate \(2f(x)\).
\[ 2f(x) = 2(5x + 3) \]

3. **Distribute the 2**: Now, distribute the 2 across the terms inside the parentheses.
\[ 2f(x) = 2 \cdot 5x + 2 \cdot 3 = 10x + 6 \]

4. **Subtract 3 from the result**: Now we need to subtract 3 from \(2f(x)\).
\[ 2f(x) - 3 = (10x + 6) - 3 \]

5. **Simplify the expression**: Combine the constants.
\[ 2f(x) - 3 = 10x + 6 - 3 = 10x + 3 \]

Thus, the expression that represents \(2f(x) - 3\) is:
\[ \boxed{10x + 3} \]