Find `k` if `fof(k)=3` where `f(k)=2k-1`.

Answer

To solve the problem of finding `k` such that `f(f(k)) = 3` where `f(k) = 2k - 1`, we can follow these steps:

### Step 1: Understand the function
We have the function defined as:
\[ f(k) = 2k - 1 \]

### Step 2: Find \( f(f(k)) \)
To find \( f(f(k)) \), we first need to substitute \( f(k) \) into itself:
\[ f(f(k)) = f(2k - 1) \]

### Step 3: Substitute into the function
Now, we need to apply the function \( f \) to \( 2k - 1 \):
\[ f(2k - 1) = 2(2k - 1) - 1 \]
\[ = 4k - 2 - 1 \]
\[ = 4k - 3 \]

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

### Step 5: Solve for \( k \)
To solve for \( k \), we first add 3 to both sides:
\[ 4k = 3 + 3 \]
\[ 4k = 6 \]

Now, divide both sides by 4:
\[ k = \frac{6}{4} \]
\[ k = \frac{3}{2} \]

### Final Answer
Thus, the value of \( k \) is:
\[ k = \frac{3}{2} \]

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