Find g(f(6)) if f(x) = -13x-11 and g(x)=14x^2+13x+11.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We are given that f(x) = -13x-11 and g(x)=14x^2+13x+11.

Now, we have to find g(f(6))

f(6) = -13x-11 = -13*6 - 11 = -89

g(f(6)) = g( -89)

= 14*(-89)^2+13*(-89)+11

= 110894 - 1157 + 11

= 109748

Therefore g(f(6)) = 109748

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To determine g(f(6)), first we'll have to determine the expression of g(f(x)).

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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