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Zorluk: KolayFunction Definitions, Evaluation, and Custom Operators

For all real numbers pp and qq, the operation ∇\nabla is defined by p∇q=2p+3q−pqp \nabla q = 2p + 3q - pq. What is the value of 3∇43 \nabla 4?

  1. A
    5
  2. 6Cevap
  3. C
    7
  4. D
    18
  5. E
    30

Cevap

The value of 3∇43 \nabla 4 is 6.
Substituting p=3p = 3 and q=4q = 4 directly into the expression 2p+3q−pq2p + 3q - pq gives 2(3)+3(4)−(3)(4)=6+12−12=62(3) + 3(4) - (3)(4) = 6 + 12 - 12 = 6.

Adım Adım Çözüm

1
Identify the assigned values for the operator inputs.
p=3p = 3 and q=4q = 4.
The expression 3∇43 \nabla 4 matches p∇qp \nabla q with pp as the first argument and qq as the second.
2
Substitute p=3p = 3 and q=4q = 4 into the custom operation formula 2p+3q−pq2p + 3q - pq.
2(3)+3(4)−(3)(4)2(3) + 3(4) - (3)(4)
Direct evaluation of the defined function rule.
3
Perform the multiplication and algebraic addition/subtraction.
6+12−12=66 + 12 - 12 = 6
Simplifying numerical operations gives the final result.

Anahtar Kavram

Custom Operator Evaluation
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Function Definitions, Evaluation, and Custom Operators

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