If the function f is defined by `f(x)=3x+2`, and if `f(a)=17`, what is the value of a?

Options

A. `5`
B. `9`
C. `10`
D. `11`

Answer

To solve the problem, we start with the function given:

1. **Write down the function**:
\( f(x) = 3x + 2 \)

2. **Substitute \( a \) into the function**:
Since we know that \( f(a) = 17 \), we substitute \( a \) into the function:
\( f(a) = 3a + 2 \)

3. **Set up the equation**:
We know that \( f(a) = 17 \), so we can set up the equation:
\( 3a + 2 = 17 \)

4. **Solve for \( a \)**:
To isolate \( a \), first subtract 2 from both sides:
\( 3a + 2 - 2 = 17 - 2 \)
\( 3a = 15 \)

5. **Divide by 3**:
Now, divide both sides by 3 to solve for \( a \):
\( a = \frac{15}{3} \)
\( a = 5 \)

Thus, the value of \( a \) is **5**.

---