Compose 2 functions f and gCompose 2 functions f and g and calculate f(g(c)). Please, give examples.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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Let us take the functions f(x) = x + 1 and g(x) = 3x to illustrate how to find f(g(x)) when f(x) and g(x) are given.

f(g(x))

as g(x) = 3x

=> f(3x)

use f(x) = x + 1

=> 3x + 1

For x = c = 2

f(g(2)) = 3*2 + 1 = 6 + 1 = 7

f(g(2)) = 7

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll consider the functions f(x) = -13x-11 and g(x)=14x^2+13x+11 and we'll determine g(f(a)).

To determine g(f(a)), first we'll have to determine the expression of g(f(x)).

We'll put a = 6

For this reason, we'll have to apply the rule of composition of 2 functions.

(gof)(x) = g(f(x))

We'll substitute x by f(x):

g(f(x)) = 14[f(x)]^2+13f(x)+11

We'll substitute f(x) by it's expression:

g(f(x)) = 14(13x+11)^2+13(-13x-11)+11

We'll expand the square and remove the brackets using the distributive law:

g(f(x)) = 14(169x^2 + 286x + 121) -169x - 143 + 11

g(f(x)) = 2366x^2 + 4004x + 1694 -169x - 143 + 11

We'll combine like terms:

g(f(x)) = 2366x^2 + 3835x + 1562

We'll determine g(f(6)):

g(f(6)) = 2366*36 + 3835*6 + 1562

g(f(6)) = 85176 + 23010 + 1562

g(f(6)) = 109748

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