Answer: -35
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Step-by-step explanation:
Let y = -3*f(-3) + 2*f(3)
The goal is to find the value of y as some single numeric value.
We know that f(x) is an odd function. This means that
f(-x) = -f(x)
For all x in the domain of f(x).
Based on that, we can say
f(-3) = -f(3)
and,
y = -3*f(-3) + 2f(3)
-1*y = -1*(-3*f(-3) + 2*f(3)) ... multiply both sides by -1
-y = 3*f(-3) - 2*f(3)
-y = 3*f(-3) + 2*(-f(3))
-y = 3*f(-3) + 2*f(-3)
-y = 3*7 + 2*7 .... f(-3) replaced with 7
-y = 21+14
-y = 35
y = -35
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Here's a slightly different approach
f(-3) = 7
-f(3) = 7
Since f(-3) = -f(3)
We can then transform -f(3) = 7 into f(3) = -7 after multiplying both sides by -1
Therefore,
y = -3*f(-3) + 2f(3)
y = -3*7 + 2(-7)
y = -21 - 14
y = -35
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There are probably other routes to solve this problem.
Whichever path you take, you should find that -3*f(-3) + 2f(3) = -35