Question

Find the inverse of the operation ( a b = 3a + 3b/ab ) if ( a b = -2 ).

a) (-1/3)
b) (-1/2)
c) (-2/3)
d) (-3/2)

Answer 1

To find the inverse of the given operation (a b = 3a + 3b/ab), we need to solve for a in terms of b. The inverse operation is a = (-2 - 3/b) / 3. None of the options provided are correct.

Step-by-step explanation:

To find the inverse of the operation (a b = 3a + 3b/ab) if (a b = -2), we need to solve for a and b in terms of -2. Let's go step by step:

1. Start with the given equation: 3a + 3b/ab = -2
2. Multiply both sides by ab to eliminate the denominator: 3a(ab) + 3b = -2(ab)
3. Distribute the ab on the right side: 3a(ab) + 3b = -2ab
4. Now, rearrange the equation to isolate a: 3a(ab) = -2ab - 3b
5. Divide both sides by 3(ab): a = (-2ab - 3b) / (3(ab))
6. Simplify the expression: a = (-2 - 3/b) / 3
7. This gives us the inverse operation: a = (-2 - 3/b) / 3

Therefore, the answer is none of the options provided.