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Find the requested composition or operation.

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4 Answers

Hi Jay,
 
f(x)=5-x
g(x)=-9x+7
 
(f+g)(x)=f(x)+g(x)
 
            =5-x-9x+7
 
            =12-10x
If you meant the sum of f(x) + g(x), then the answers below are correct.  If you meant the composition of f(x) and g(x), that is f(g(x)) or f ° g, then substitute g(x) for x in f(x):
 
f ° g = 5 - (-9x + 7) = 9x - 2
 
Note that composition does not obey the associative law, that is f ° g does not equal g ° f
Given
f(x) = 5 - x
g(x) = -9x + 7

(f + g)(x)
 
f(x) + g(x) = (5 - x) + (-9x + 7)
 
f(x) + g(x)  = (5 - x - 9x +7)
 
f(x) + g(x)  = (12 - 10x)
 
this can be rewritten as;
 
(f + g)(x) = (12 - 10x)
(f+g)(x) is the same as f(x) + g(x).
 
It is just slightly shorter notation, and removes any confusion as to whether f and g use the same variable when evaluating.