The function \( f(x) = 35x + 50 \) represents the cost of gym membership after \( x \) months, where:
- \( 35x \) is the variable cost depending on the number of months (with \( 35 \) being the monthly fee),
- \( 50 \) is the fixed cost or one-time membership fee.
The initial value of the function, which occurs when \( x = 0 \), is \( f(0) = 35(0) + 50 = 50 \).
Thus, the correct interpretation is:
The initial value of 50 represents the one-time membership fee.