Compose 2 functions f and gCompose 2 functions f and g and calculate f(g(c)). Please, give examples.
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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 | College Teacher | (Level 3) Valedictorian
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