To solve for the variable \( f \) in the equation
\[ \frac{17}{3f - 1} = 1, \]
we can start by eliminating the fraction. We do this by multiplying both sides of the equation by \( 3f - 1 \):
\[ 17 = 1 \cdot (3f - 1). \]
This simplifies to:
\[ 17 = 3f - 1. \]
Next, we can add 1 to both sides of the equation:
\[ 17 + 1 = 3f, \]
which simplifies to:
\[ 18 = 3f. \]
Now, to isolate \( f \), we divide both sides by 3:
\[ f = \frac{18}{3}. \]
This simplifies to:
\[ f = 6. \]
So, the value of \( f \) is
\[ \boxed{6}. \]