SOLUTION: 7. Let f(x) = to x squared - 6x + 9 ,g(x) = x - 3 find the following. a.(f+g)(x) b.(f-g)(x) c.(fg)(x) d. (f/g)(x) e.(fog)(x) f.(f-g)(5) g.g{f(x)} h. f

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 7. Let f(x) = to x squared - 6x + 9 ,g(x) = x - 3 find the following. a.(f+g)(x) b.(f-g)(x) c.(fg)(x) d. (f/g)(x) e.(fog)(x) f.(f-g)(5) g.g{f(x)} h. f      Log On


   

Question 128321: 7. Let f(x) = to x squared - 6x + 9 ,g(x) = x - 3 find the following.


a.(f+g)(x) b.(f-g)(x) c.(fg)(x) d. (f/g)(x) e.(fog)(x)
f.(f-g)(5) g.g{f(x)} h. f{f(-3)}



Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)

Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 and g%28x%29=x-3

Group like terms


Combine like terms



So
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b)



Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 and g%28x%29=x-3


Distribute the negative


Group like terms


Combine like terms


So
------------------------------------------------------------------------


c)




Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 and g%28x%29=x-3



Rearrange the terms



Expand the expression. Remember something like %28a%2Bb%29%28c%2Bd%2Be%29 expands to a%28c%2Bd%2Be%29%2Bb%28c%2Bd%2Be%29


Distribute



Combine like terms


So
------------------------------------------------------------------------



d)



Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 and g%28x%29=x-3



Factor x%5E2-6x%2B9 to get %28x-3%29%28x-3%29



Divide and simplify. Note: x%3C%3E3



So

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e)





Start with the given property

Plug in g%28x%29=x-3 into each x of f%28x%29=x%5E2-6x%2B9




Foil



Distribute



Combine like terms



So

------------------------------------------------------------------------

f)


Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 and g%28x%29=x-3


Plug in x=5


Multiply


Combine like terms


Subtract




So
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g)




Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 into each x of g%28x%29=x-3


Combine like terms


So
------------------------------------------------------------------------

h)




Start with the given property

Plug in f%28x%29=x%5E2-6x%2B9 into each x of f%28x%29=x%5E2-6x%2B9



Now plug in x=-3


Multiply and square the given values



Add


Multiply and square the values


Combine like terms



So