How do you find $[f o g] (x)$ $[fog](x)$ and $[g o f] (x)$ $[gof](x)$ given $f (x) = 2 x + 5$ $f(x)=2x+5$ and $g (x) = 3 + x$ $g(x)=3+x$ ?

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Answer 1 · 2017-03-06T17:13:37

The answers are $[f o g] (x) = 2 x + 11$ $[fog] (x)=2x+11$ and $[g o f] (x) = 2 x + 8$ $[gof] (x)=2x+8$

This is a composition of functions

$f (x) = 2 x + 5$ $f(x)=2x+5$

$g (x) = 3 + x$ $g(x)=3+x$

$[f o g] (x) = f (g (x)) = f (3 + x) = 2 (3 + x) + 5$ $[fog] (x) =f(g(x))=f(3+x)=2(3+x)+5$

$= 6 + 2 x + 5 = 2 x + 11$ $=6+2x+5=2x+11$

And

$[g o f] (x) = g (f (x)) = g (2 x + 5) = 3 + 2 x + 5$ $[gof ] (x)=g(f(x))=g(2x+5)=3+2x+5$

$= 2 x + 8$ $=2x+8$

How do you find [fog](x)[fog](x) and [gof](x)[gof](x) given f(x)=2x+5f(x)=2x+5 and g(x)=3+xg(x)=3+x?