Question

A function, \( \lambda \), is defined by \[ \lambda ( p,q ) = \begin{cases} (p - q)^2, & \text{if } p \geq q, \\ p + q, & \text{if } p < q. \end{cases} \] The value of the expression \( \dfrac{\lambda ( -(-3 + 2), (-2 + 3) )}{( -(-2 + 1) )} \) is:

• A. \( -1 \)
• B. 0
• C. \( \frac{16}{3} \)
• D. \( 16 \)

Hint:

When working with piecewise functions, carefully evaluate which case to use based on the given condition.

Answer 1

The Correct Option is B

We are given the function \( \lambda(p, q) \) defined in two parts, depending on the relationship between \( p \) and \( q \). First, we simplify the values inside the function: \[ \lambda( -3 + 2, -2 + 3 ) = \lambda( -1, 1 ). \] Since \( p = -1 \) and \( q = 1 \), we have \( p < q \), so we use the second case of the function, where \( \lambda(p, q) = p + q \). Thus: \[ \lambda( -1, 1 ) = -1 + 1 = 0. \] Therefore, the value of the expression is \( 0 \). Final Answer: \( 0 \)