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QuestionEvaluate G(−1)G(-1), G(2)G(2), and compute [G(−1)]3−[G(2)]2+4⋅G(−1)=20[G(-1)]^{3}-[G(2)]^{2}+4 \cdot G(-1)=20.

Studdy Solution

STEP 1

Assumptions1. The function G(x) is given such that G(-1) =20 and G() =10. . We are asked to evaluate the expression [G(-1)]^{3}-[G()]^{}+4 \cdot G(-1).

STEP 2

The values of G(-1) and G(2) are given. We can substitute these values into the expression.
[G(−1)]−[G(2)]2+4⋅G(−1)=[20]−[10]2+4⋅20[G(-1)]^{}-[G(2)]^{2}+4 \cdot G(-1) = [20]^{}-[10]^{2}+4 \cdot20

STEP 3

Now, we can calculate the value of the expression by following the order of operations, which is parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). This is often abbreviated as PEMAS.
[G(−1)]3−[G(2)]2+⋅G(−1)=[20]3−[10]2+⋅20=8000−100+80[G(-1)]^{3}-[G(2)]^{2}+ \cdot G(-1) = [20]^{3}-[10]^{2}+ \cdot20 =8000 -100 +80

STEP 4

Finally, we can simplify the expression by performing the addition and subtraction from left to right.
[G(−1)]3−[G(2)]2+4⋅G(−1)=8000−100+80=7980[G(-1)]^{3}-[G(2)]^{2}+4 \cdot G(-1) =8000 -100 +80 =7980So, the value of the expression [G(-1)]^{3}-[G(2)]^{2}+4 \cdot G(-1) is7980.

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