Question

Find the inverse of each function and show work.

G(n)= 2/3 n+2

A. G⁻¹(n) = -4 + 1/3 n

B. A. G⁻¹(n) = -4 + 8/5n

C. G⁻¹(n) = -3 + 3/2 n

D. G⁻¹(n) = 5n + 5/4 −1

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Answer 1

To find the inverse of the function G(n) = (2/3)n + 2, we perform operations in reverse, resulting in the inverse function G⁻¹(n) = (3/2)n - 3, matching option C.

Step-by-step explanation:

To find the inverse function of G(n), we want to solve for n in terms of the output (let's call it 'y' for the moment). Starting with G(n) = (2/3)n + 2, we substitute G(n) with y to get y = (2/3)n + 2. To find the inverse, we need to 'undo' each operation that has been done to 'n' in reverse order.

1. Subtract 2 from both sides of the equation: y - 2 = (2/3)n.
2. Multiply both sides by the reciprocal of (2/3) to solve for n: (3/2)(y - 2) = n.
3. Simplify the right side, resulting in n = (3/2)y - 3.
4. Now represent the inverse function: G⁻¹(n) = (3/2)n - 3.

Therefore, the correct inverse function is G⁻¹(n) = (3/2)n - 3, which matches option C.