Question

Read the information given below and answer the questions that follow:
A, S, M and D are functions of x and y, and they are defined as follows:
A (x, y) = x + y
S (x, y) = x – y
M (x, y) = xy
D (x, y) = $\frac{x}{y}$ where y is not equal to 0.

What is the value of S[M (D(A(a,b),2),D(A(a,b),2)),M(D(S(a,b),2),D(S(a,b),2))]?

• A. a² + b²
• B. ab
• C. a² – b²
• D. a / b

Answer 1

The correct option is B ab

Soln: (b)

S [M (D (A (a, b),2), D (A (a, b), 2)), M (D (S (a, b), 2), D (S (a, b), 2))]

S [M (D (a + b, 2), D (a + b, 2)), M (D (a – b, 2),D (a – b, 2))]

S [M[$\frac{(a+b)}{2}$, $\frac{(a+b)}{2}$], M( $\frac{a-b}{2},\frac{a-b}{2}$)]

S [ ${\left(\frac{a+b}{2}\right)}^2,{\left(\frac{a-b}{2}\right)}^2]=\frac{\left[\right(a+b{)}^2-(a-b{)}^2]}{2^2}$

$=\frac{\left(2a\right)\left(2b\right)}{4}=ab$