f(-9)

f(x+1)

f(-x)

f(-9)

f(x+1)

f(-x)

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We need to evaluate the function, f(x) = x^{2}+2x+3, by substituting f(-9), f(x+1) and f(-x). This means that we substitute the values given to us in place of each x in the equation.

So the value, f(-9), means we will substitute -9 in the original equation for x:

f(-9) = (-9)^{2}+2(-9)+3

f(-9) = 81-18+3 = 66

So **f(-9) = 66**

The next value we substitute for x is (x+1), so each x value in the equation becomes (x+1):

f(x+1) = (x+1)^{2}+2(x+1)+3

f(x+1) = (x+1)^{2 }+2x+2+3

f(x+1) = (x+1)^{2}+2x+5

We can go further and use the FOIL method to solve (x+1)^{2} because it may also be written as

(x+1)(x+1).

We FOIL that portion of the equation and add the rest of the equation to it to get:

f(x+1) = **(x ^{2}+1x+1x+1)** +2x+5

Now simplify and combine like terms to get our final answer for f(x+1):

**f(x+1) = x2 +4x+6**

Lastly, we solve for the value f(-x) by substituting -x for x:

f(-x) = (-x)^{2}+2(-x)+3

**f(-x) = x-2x+3**

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