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composition of functions Find f(f(4)) if f(x)=14x+13.

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Tushar Chandra eNotes educator | Certified Educator

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It is given that f(x)=14x+13.

f(f(4))

given that f(4) = 14*4 + 13

=> f( 14*4 + 13)

=> f(69)

=> 14*69 + 13

=> 979

The value of f(f(4))  = 979

 

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giorgiana1976 | Student

To find out f(f(4)), first we'll have to determine the expression of f(f(x)).

This problem requests to apply the rule of composition of 2 functions.

(fof)(x) = f(f(x))

We'll substitute x by f(x):

f(f(x)) = 14*f(x)+13

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

f(f(x)) = 14(14x + 13) + 13

We'll remove the brackets using the distributive law:

f(f(x)) = 196x + 182 + 13

f(f(x)) = 196x + 195

We'll determine f(f(4)):

f(f(4)) = 196*4 + 195

f(f(4)) = 979