SOLUTION: for the function f defined by f(x)=4x^2+5x+9, find the following values: a. f(-2)= b. f(-x)= c.-f(x)= d. f(x+h)= I could really use some help with how to solve this!

Algebra ->  Rational-functions -> SOLUTION: for the function f defined by f(x)=4x^2+5x+9, find the following values: a. f(-2)= b. f(-x)= c.-f(x)= d. f(x+h)= I could really use some help with how to solve this!       Log On


   

Question 625611: for the function f defined by f(x)=4x^2+5x+9, find the following values:
a. f(-2)=
b. f(-x)=
c.-f(x)=
d. f(x+h)=
I could really use some help with how to solve this!
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
.
The Problem:
For the function f defined by f(x)=4x^2+5x+9, find the following values:
a. f(-2)=
b. f(-x)=
c.-f(x)=
d. f(x+h)=

Solution:
These are actually much easier to do than you might think. One challenging part can be 
dealing with the negative signs. Let's start with the first one.

a. Find f(-2)

Start with the function f and substitute -2 for x in the right hand side.
f%28x%29=4x%5E2%2B5x%2B9
f%28-2%29+=+4%28-2%29%5E2%2B5%28-2%29%2B9

Clear the parentheses on the right hand side; (-2) squared is 4 because (-2)(-2)=4.
f%28-2%29=4%284%29%2B%28-10%29%2B9
f%28-2%29=16-10%2B9

Add the constant terms on the right hand side.
f%28-2%29=15

I'll set up the others for you. 

b.f%28-x%29=4%28-x%29%5E2%2B5%28-x%29%2B9
Remember that (-x) squared is x^2.

c. -f%28x%29=-%284x%5E2-5x%2B9%29
Distribute the negative sign across every term on the right hand side.

d. f%28x%2Bh%29+=+4%28x%2Bh%29%5E2-5%28x%2Bh%29+%2B9
This is the most complex substitution of the set. However, if you plan to take calculus, the f(x+h) 
substitution is one you will do A LOT...good to practice now.

Try these on your own. Email me if you have questions or if you want me to check your answers.

Ms.Figgy
math.in.the.vortex@gmail.com