Question

A, S, M, and D are functions of \( x \) and \( y \), and they are defined as follows: \[ A(x, y) = x + y, \quad S(x, y) = x - y \] \[ M(x, y) = x \cdot y, \quad D(x, y) = \frac{x}{y}, \quad y \neq 0 \] What is the value of \( M(M(A(M(x, y), S(x, y)), D(x, y)), A(x, y)) \) for \( x = 2 \), \( y = 3 \)?

• A. 60
• B. 140
• C. 25
• D. 70

Hint:

Break down complex expressions step by step and apply the functions sequentially.

Answer 1

The Correct Option is B

We need to find the value of the expression: \[ M(M(A(M(x, y), S(x, y)), D(x, y)), A(x, y)) \] Substitute \( x = 2 \) and \( y = 3 \) into the functions: \[ A(2, 3) = 2 + 3 = 5, \quad S(2, 3) = 2 - 3 = -1 \] \[ M(2, 3) = 2 \times 3 = 6, \quad D(2, 3) = \frac{2}{3} \] Now, calculate the innermost function: \[ M(A(M(2, 3), S(2, 3))) = M(A(6, -1)) = M(6 + (-1)) = M(5) = 5 \times 5 = 25 \] Next, apply \( D(2, 3) = \frac{2}{3} \): \[ M(25, \frac{2}{3}) = 25 \times \frac{2}{3} = \frac{50}{3} = 16.67 \] Finally, apply \( A(2, 3) = 5 \): \[ M(16.67, 5) = 16.67 \times 5 = 140 \] Thus, the answer is b. 140.