For all real numbers a and b, a custom operation \ast is defined by a \ast b = a^2 - 2b. W… — ACT

For all real numbers $a$ and $b$ , a custom operation $\ast$ is defined by $a \ast b = a^2 - 2b$ . What is the value of the expression $2 \ast (3 \ast 4)$ ?

2Answer
B
-4
C
8
D
-52
E
-3

Answer

Evaluating the parentheses first gives

3 \ast 4 = 3^2 - 2(4) = 9 - 8 = 1

. Substituting this back into the expression yields

2 \ast 1

. Evaluating this gives

2^2 - 2(1) = 4 - 2 = 2

, which is the correct value.

Step-by-Step Solution

Evaluate the expression inside the parentheses:

3 \ast 4

3 \ast 4 = 3^2 - 2(4) = 9 - 8 = 1

According to the order of operations, expressions inside parentheses must be evaluated first.

Substitute the result back into the main expression.

2 \ast (3 \ast 4) = 2 \ast 1

The evaluated value of the parentheses is substituted back to continue solving.

Evaluate

2 \ast 1

using the operation definition.

2 \ast 1 = 2^2 - 2(1) = 4 - 2 = 2

Applying the definition of the custom operation to the remaining terms yields the final answer.

Key Concept

Order of Operations and Custom Arithmetic Operations

Estimated Time:1m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic