Find `k` if `fof(k)=3` where `f(k)=2k-6`

Answer

To solve the equation \( f(f(k)) = 3 \) where \( f(k) = 2k - 6 \), we will follow these steps:

### Step 1: Find \( f(f(k)) \)
First, we need to find \( f(f(k)) \). We start by substituting \( f(k) \) into itself.

Given:
\[ f(k) = 2k - 6 \]

Now, substitute \( f(k) \) into \( f \):
\[ f(f(k)) = f(2k - 6) \]

### Step 2: Substitute into \( f \)
Now we will apply the function \( f \) to \( 2k - 6 \):
\[ f(2k - 6) = 2(2k - 6) - 6 \]

### Step 3: Simplify the expression
Now, simplify the expression:
\[ = 4k - 12 - 6 \]
\[ = 4k - 18 \]

### Step 4: Set the equation equal to 3
Now we set \( f(f(k)) \) equal to 3:
\[ 4k - 18 = 3 \]

### Step 5: Solve for \( k \)
Now, we will solve for \( k \):
\[ 4k - 18 + 18 = 3 + 18 \]
\[ 4k = 21 \]
\[ k = \frac{21}{4} \]

### Final Answer
Thus, the value of \( k \) is:
\[ k = \frac{21}{4} \]

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