For all real numbers p and q, the custom operation \odot is defined by p \odot q = 2p^2 - … — GRE General Test

For all real numbers $p$ and $q$ , the custom operation $\odot$ is defined by $p \odot q = 2p^2 - 3q$ . What is the value of $3 \odot (-4)$ ?

Answer: 30

The value of

3 \odot (-4)

30

By applying the definition of the custom operation

p \odot q = 2p^2 - 3q

with

p = 3

and

q = -4

, we obtain

2(3)^2 - 3(-4) = 2(9) + 12 = 18 + 12 = 30

Substitute

p = 3

and

q = -4

into the expression

2p^2 - 3q

2(3)^2 - 3(-4)

The custom operation defines how to process the two inputs

p

and

q

Simplify the powers and products according to order of operations.

2(9) - (-12) = 18 + 12

Exponents must be calculated before multiplication, and multiplying two negative numbers yields a positive value.

Add the terms together to get the final numerical result.

30

18 + 12 = 30

Custom Symbol Operations

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