Question

Help with this please

Answer 1

Answer:    -35

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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