Question

Difficulty: EasyFunction Definitions, Evaluation, and Custom Operators

For all real numbers $p$ and $q$ , the operation $\nabla$ is defined by $p \nabla q = 2p + 3q - pq$ . What is the value of $3 \nabla 4$ ?

The value of

3 \nabla 4

is 6.

Substituting

p = 3

and

q = 4

directly into the expression

2p + 3q - pq

gives

2(3) + 3(4) - (3)(4) = 6 + 12 - 12 = 6

Identify the assigned values for the operator inputs.

p = 3

and

q = 4

The expression

3 \nabla 4

matches

p \nabla q

with

p

as the first argument and

q

as the second.

Substitute

p = 3

and

q = 4

into the custom operation formula

2p + 3q - pq

2(3) + 3(4) - (3)(4)

Direct evaluation of the defined function rule.

Perform the multiplication and algebraic addition/subtraction.

6 + 12 - 12 = 6

Simplifying numerical operations gives the final result.

Custom Operator Evaluation

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