Find the requested composition or operation.

Question

f(x) = 5-x, g(x) = -9x+7

Find (f + g)(x).

Answer 1

Hi Jay,

 

f(x)=5-x

g(x)=-9x+7

 

(f+g)(x)=f(x)+g(x)

 

            =5-x-9x+7

 

            =12-10x

Answer 2

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

Answer 3

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)

Answer 4

(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.