Question

Difficulty: EasyFunction Definitions, Evaluation, and Custom Operators

For all real numbers $x$ and $y$ , the custom operation $\diamondsuit$ is defined by $x \diamondsuit y = 3x - 2y + 1$ . What is the value of $5 \diamondsuit 4$ ?

Answer: 8

Answer

The value of

5 \diamondsuit 4

is 8.

Substituting

x = 5

and

y = 4

into the operation

x \diamondsuit y = 3x - 2y + 1

yields

3(5) - 2(4) + 1 = 15 - 8 + 1 = 8

Step-by-Step Solution

Substitute the operands into the custom operator rule

5 \diamondsuit 4 = 3(5) - 2(4) + 1

The first term

5

corresponds to

x

and the second term

4

corresponds to

y

in the formula.

Simplify the numeric expression

15 - 8 + 1 = 8

Multiply first, then perform subtraction and addition from left to right.

Key Concept

Function Definitions, Evaluation, and Custom Operators

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