Find `k` if `fof(k)=4` where `f(k)=3k-2`.

Answer

To solve for \( k \) in the equation \( f(f(k)) = 4 \) where \( f(k) = 3k - 2 \), follow these steps:

### Step 1: Define the function
We have the function:
\[ f(k) = 3k - 2 \]

### Step 2: Find \( f(f(k)) \)
To find \( f(f(k)) \), we first need to substitute \( f(k) \) into itself:
\[ f(f(k)) = f(3k - 2) \]

### Step 3: Substitute \( 3k - 2 \) into \( f(k) \)
Now we need to calculate \( f(3k - 2) \):
\[ f(3k - 2) = 3(3k - 2) - 2 \]
Distributing the 3:
\[ = 9k - 6 - 2 \]
Combining like terms:
\[ = 9k - 8 \]

### Step 4: Set the equation to 4
Now we set \( f(f(k)) \) equal to 4:
\[ 9k - 8 = 4 \]

### Step 5: Solve for \( k \)
Add 8 to both sides:
\[ 9k = 4 + 8 \]
\[ 9k = 12 \]
Now, divide both sides by 9:
\[ k = \frac{12}{9} = \frac{4}{3} \]

### Final Answer
Thus, the value of \( k \) is:
\[ \boxed{\frac{4}{3}} \]