How do you find the compositions given $f (x) = x + 5$ $f(x)=x + 5$ , $g (x) = 2 x$ $g(x)= 2x$ , $h (x) = x - 2$ $h(x)= x-2$ ?

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Answer 1 · 2017-04-27T20:15:05

There are many compositions that you can perform with 3 functions, each time, you will substitute one expression into the other.

Example 1: f(g(x)) = 2x + 5 because 2x replaces x.

Example 2: g(f(x)) = 2(x + 5) because x + 5 replaces x.

Example 3: g(h(x)) = 2(x - 2) because x - 2 replaces x.

Example 4: h(f(x)) = (x + 5) - 2 or x + 3 since x + 5 replaces x.

How do you find the compositions given f(x)=x + 5f(x)=x+5f(x)=x + 5, g(x)= 2xg(x)=2xg(x)= 2x, h(x)= x-2h(x)=x−2h(x)= x-2?