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

Find (f + g)(x).

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

Find (f + g)(x).

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Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...

Hi Jay,

f(x)=5-x

g(x)=-9x+7

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

=5-x-9x+7

=12-10x

Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor

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 + 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.

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