f(-9)
f(x+1)
f(-x)
f(-9)
f(x+1)
f(-x)
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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