If 5 # 3 = 19 and 7 # 2 = 17, what is 9 # 1?

To find the value of 9 # 1, we first identify the functional pattern connecting the numbers provided in the examples: 5 # 3 = 19 and 7 # 2 = 17.

Analysis of the Pattern
By testing various operations, we find that the pattern follows the rule: (a × b) + (b + 1), where a is the first number and b is the second number.

Example 1: 5 # 3 = (5 × 3) + (3 + 1) = 15 + 4 = 19

Example 2: 7 # 2 = (7 × 2) + (2 + 1) = 14 + 3 = 17

Target Calculation: 9 # 1 = (9 × 1) + (1 + 1) = 9 + 2 = 11