If f(x)=2x-1, find the value of x that makes f(f(x))=9.

Options

A. 2
B. 3
C. 4
D. 5

Explanation

To solve the problem where \( f(x) = 2x - 1 \) and we need to find the value of \( x \) that makes \( f(f(x)) = 9 \), we can follow these steps:

### Step 1: Find \( f(f(x)) \)
We start by calculating \( f(f(x)) \). Since \( f(x) = 2x - 1 \), we need to substitute \( f(x) \) into itself:

\[ f(f(x)) = f(2x - 1) \]

### Step 2: Substitute into the function
Now we substitute \( 2x - 1 \) into the function \( f \):

\[ f(2x - 1) = 2(2x - 1) - 1 \]

### Step 3: Simplify the expression
Next, we simplify the expression:

\[ = 4x - 2 - 1 \]
\[ = 4x - 3 \]

### Step 4: Set the equation equal to 9
Now we set \( f(f(x)) \) equal to 9:

\[ 4x - 3 = 9 \]

### Step 5: Solve for \( x \)
To solve for \( x \), we first add 3 to both sides:

\[ 4x = 9 + 3 \]
\[ 4x = 12 \]

Now, divide both sides by 4:

\[ x = \frac{12}{4} \]
\[ x = 3 \]

### Final Answer
The value of \( x \) that makes \( f(f(x)) = 9 \) is \( x = 3 \).

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