How do you find the compositions given $f(x)=7x+4$ and $g(x)=x-7$ ?

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Answer 1 · 2015-12-29T19:52:00

$f(x)=7x+4$ , $g(x)=x-7$

There can be infinite compositions.

I hope you are talking about the following two compositions.
$(i)$ $f(g(x))$
$(ii)$ $(g(f(x))$

$(i)$ $f(g(x))=f(x-7)=7(x-7)+4=7x-49+4=7x-45$
$implies f(g(x))=7x-45$

$(ii)$ $g(f(x))=g(7x+4)=7x+4-7=7x-3$
$implies g(f(x))=7x-3$

How do you find the compositions given f(x)=7x+4f(x)=7x+4 and g(x)=x-7g(x)=x-7?