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LostInParadise's avatar

Any suggestions on how to explain function composition in algebra?

Asked by LostInParadise (24855points) November 6th, 2016

I do some online tutoring and I have found that some students have a hard time with the idea of composing two functions. For example, if f(x)=3x+2 and g(x)=x+1, then f(g(x)) is 3(x+1)+2.

I tried the following, but it did not seem to work. f(g(x)) = 3(g(x)) + 1 = 3(x+1) + 2. Any other ideas? I was thinking that if students were taught to program a language like Python then the two functions could be translated into two software functions and it might be clearer.

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4 Answers

Zissou's avatar

I think there is an error here where you write… = 3(g(x)) + 1 = ... that + 1 there should be a + 2, right?

Maybe try writing the functions in different colors or fonts to emphasize how the one plugs right into the other.

Mariah's avatar

My precalc teacher did this great as part of basic function substitution. Basically:

F(x) = x+3
F(t) = ? (Someone raises their hand, substitutes in t+3.
F(7) = 7+3 = 10.
F(☺️) = ☺️ + 3 (good absurd example showing you to just blindly substitute what’s in the parens).
F(x+2) = x +2 +3 = x + 5
G(x) = x + 2
F(G(x)) = x + 2 + 3 = x + 5

LostInParadise's avatar

I will give that a try next time.

dxs's avatar

When I try explaining it, I write out the original function and then circle with red the x’s. Then, I write the function composition underneath and circle the g(x)‘s, to show that you’re putting it into the function in the same way.
I wish we could show them rotations and reflections. That might help them understand it. Or maybe not.

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