Evaluate the function f(x)=x^2+2x+3 at the given values of the independent variable and simplivy

Question

f(-9)

f(x+1)

f(-x)

Answer 1

We need to evaluate the function, f(x) = x²+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) = (x²+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