Given f, of, x, equals, 4, x, minus, 3*f*(*x*)=4*x*−3, solve for x*x* when f, of, x, equals, 9*f*(*x*)=9.

To solve for \( x \) when \( f(x) = 9 \), we start by using the given function definition:
\[
f(x) = 4x - 3
\]

### Step 1: Set up the Equation
Since \( f(x) = 9 \), substitute \( 9 \) for \( f(x) \) in the equation:
\[
4x - 3 = 9
\]

### Step 2: Solve for \( x \)
1. **Add 3 to both sides**:
   \[
   4x - 3 + 3 = 9 + 3
   \]
   \[
   4x = 12
   \]

2. **Divide by 4**:
   \[
   x = \frac{12}{4}
   \]
   \[
   x = 3
   \]

Therefore, the solution is:
\[
x = 3
\]

Would you like additional details or have any questions about this solution? 

### Related Questions
1. What is the process for finding the inverse of \( f(x) = 4x - 3 \)?
2. If \( f(x) = 2x + 1 \), what is the solution for \( f(x) = 9 \)?
3. How can we check if \( f(x) = 4x - 3 \) is a one-to-one function?
4. How do we graph \( f(x) = 4x - 3 \) and identify its key features?
5. What are the solutions if \( f(x) = 4x - 3 = 15 \) instead?

#### Tip:
Always check your solutions by substituting back into the original function to ensure they satisfy the given conditions.

Given f(x) = 4x - 3, solve for x when f(x) = 9.

Learn how to solve the linear equation f(x) = 4x - 3 when f(x) = 9 with a clear, step-by-step solution. This algebra problem covers linear functions and is suitable for students in Grades 9-10.

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