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Math  /  Algebra

Question=−2(3x−1)2+7/f(8)=-2(3 x-1)^{2}+7 / f(8) d) f(x)=−∣−x3−2∣+5,f(−1)\quad f(x)=-\left|-x^{3}-2\right|+5, f(-1)

Studdy Solution

STEP 1

1. We are given a function f(x)=−∣−x3−2∣+5 f(x) = -\left|-x^3 - 2\right| + 5 .
2. We need to evaluate this function at x=−1 x = -1 .
3. The absolute value function outputs the non-negative value of its input.

STEP 2

1. Substitute x=−1 x = -1 into the function.
2. Simplify the expression inside the absolute value.
3. Evaluate the absolute value.
4. Complete the calculation to find f(−1) f(-1) .

STEP 3

Substitute x=−1 x = -1 into the function f(x) f(x) :
f(−1)=−∣−(−1)3−2∣+5 f(-1) = -\left|-(-1)^3 - 2\right| + 5

STEP 4

Simplify the expression inside the absolute value:
(−1)3=−1 (-1)^3 = -1 −(−1)3=1 -(-1)^3 = 1 1−2=−1 1 - 2 = -1
So, the expression inside the absolute value becomes −1-1.

STEP 5

Evaluate the absolute value:
∣−1∣=1 \left|-1\right| = 1

STEP 6

Complete the calculation to find f(−1) f(-1) :
f(−1)=−1+5=4 f(-1) = -1 + 5 = 4
The value of f(−1) f(-1) is 4 \boxed{4} .

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