If `f(x)=3x+4` then: `f((x-4)/(3))=`

Options

A. 1
B. x
C. 0
D. none of these.

Answer

To solve the problem, we need to find \( f\left(\frac{x-4}{3}\right) \) given that \( f(x) = 3x + 4 \).

### Step-by-Step Solution:

1. **Identify the function**: We have the function \( f(x) = 3x + 4 \).

2. **Substitute the expression into the function**: We need to find \( f\left(\frac{x-4}{3}\right) \). This means we will replace \( x \) in the function \( f(x) \) with \( \frac{x-4}{3} \).

3. **Write the substitution**:
\[ f\left(\frac{x-4}{3}\right) = 3\left(\frac{x-4}{3}\right) + 4 \]

4. **Simplify the expression**:
- First, calculate \( 3 \left(\frac{x-4}{3}\right) \):
\[ 3 \left(\frac{x-4}{3}\right) = x - 4 \]
- Now, add 4 to this result:
\[ x - 4 + 4 = x \]

5. **Final result**: Therefore, we have:
\[ f\left(\frac{x-4}{3}\right) = x \]

### Final Answer:
\[ f\left(\frac{x-4}{3}\right) = x \]

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