Consider the function f(x) = 2x^2 - 4x + 9. Evaluate 2f(3) + 3f(-3).

Answer: 147

Step-by-step explanation:

To evaluate 2f(3)+3f(-3), we first need to find the values of f(3) and f(-3). Given f(x), we just plug in x=3, -3 into f(x).

f(3)=2(3)²-4(3)+9         [exponent]

f(3)=2(9)-4(3)+9          [parenthesis]

f(3)=18-12+9                [subtract]

f(3)=6+9                       [add]

f(3)=15

Now, we find f(-3).

f(-3)=2(-3)²-4(-3)+9      [exponent]

f(-3)=2(9)-4(-3)+9         [parenthesis]

f(-3)=18+12+9               [add]

f(-3)=30+9                    [add]

f(-3)=39

With the values of f(3) and f(-3), we can evaluate the expression.

2(15)+3(39)                  [multiply]

30+117                          [add]

147

Now, we know the value is 147.

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