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Composition of Functions Worksheet Form

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G ( x)  x 2 , 12. find  f  g 3 11. (g◦f)(x) 13. If f ( x)  9 x  9 and g ( x)  x  9 , find  f  g 10 14. 16. If f ( x)  4 x  2 and g ( x)  x  8 , find  f  g 12 If f ( x)  2 x  1 and g ( x)  x 2  5 , find g  f 2 Given f ( x)  2 x  5 and g ( x)  x  2, 18. find  f  g x  Given f ( x)  4 x  3 and g ( x)  x 2 , 20. find g  f x  If f ( x)  3x  4 and g ( x)  x 2 , 15. find g  f  2 Given f ( x)  9 x  3 and g ( x)  x 4...
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Now in this lesson we're going to talk about composite functions so let's say that f of X is equal to 3x minus 4 and that G of X let's say it's equal to x squared minus 3 what is f of G notice that this is different from F times G if you see a closed circle it's multiplication it's 3 X minus 4 times x squared minus 3 but if you see like an open circle what it means is its a composite function one function is inside another G is inside F, so this is equivalent to F of G of X so how can we find F of G of X well let's replace G the G is x squared minus 3 and notice that x squared minus 3 is inside F, so we're going to have to replace X with x squared minus 3, so this is going to be 3 times x squared minus 3 minus 4 so now let's distribute the 3, so that's 3x squared minus 9 minus 4 which is 3 x squared minus 13 now what about G of F how can we find the value of G of F so this time F is inside G, so you can write it like this that's an equivalent expression and let's replace f of X with 3x

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