For all real numbers x and y, the custom operation \odot is defined by x \odot y = x^2 - 2… — GMAT

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

Following the explicit operator rule

x \odot y = x^2 - 2y

, first calculate the inner expression

(3 \odot 2) = 3^2 - 2(2) = 5

. Next, substitute 5 into the outer expression to compute

5 \odot 4 = 5^2 - 2(4) = 25 - 8 = 17

. Thus, the value 17 is correct.

Evaluate the inner function expression

(3 \odot 2)

using the rule

x \odot y = x^2 - 2y

3 \odot 2 = 3^2 - 2(2) = 9 - 4 = 5

Parentheses dictate that inner custom operations must be evaluated first.

Substitute the result of step 1 back into the expression to evaluate

5 \odot 4

5 \odot 4 = 5^2 - 2(4) = 25 - 8 = 17

Applying the custom operator rule with

x = 5

and

y = 4

computes the final target value.

Custom Operator Evaluation and Order of Operations

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