If $f (x) = - 2 x + 11$ $f(x)=-2x+11$ and $g (x) = x - 6$ $g(x)=x-6$ , how do you find $[f o g] (x)$ $[fog](x)$ and $[g o f] (x)$ $[gof](x)$ ?

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Answer 1 · 2016-11-09T15:51:27

The answers are $f o g (x) = - 2 x + 23$ $fog(x)=-2x+23$ and $g o f (x) = - 2 x + 5$ $gof(x)=-2x+5$

$f (x) = - 2 x + 11$ $f(x)=-2x+11$

$g (x) = x - 6$ $g(x)=x-6$

$f o g (x) = f (g (x)) = f (x - 6) = - 2 (x - 6) + 11$ $fog(x)=f(g(x))=f(x-6)=-2(x-6)+11$
$= - 2 x + 12 + 11 = - 2 x + 23$ $=-2x+12+11=-2x+23$

$g o f (x) = g (f (x)) = g (- 2 x + 11) = - 2 x + 11 - 6$ $gof(x)=g(f(x))=g(-2x+11)=-2x+11-6$
$= - 2 x + 5$ $=-2x+5$

I think that the equations speak by themselves.

Of course, $f o g (x) \neq g o f (x)$ $fog(x)!=gof(x)$

If f(x)=-2x+11f(x)=−2x+11f(x)=-2x+11 and g(x)=x-6g(x)=x−6g(x)=x-6, how do you find [fog](x)[fog](x)[fog](x) and [gof](x)[gof](x)[gof](x)?