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For g o h(x) take h and SHOVE IT into g g o h(x) = 2(x 2) = 2x 4 Same for h o g(x) take g and SHOVE IT into h h o g(x) = (2x) 2 = 2x 2. A C h N G C V Ђ͐M Ǝ тɊ Â A r o c ̐V ȓW J n ܂ B s Y ƕ F ݁E A R T e B O A t H. X v ւ̗v E j ɂ L ܂ 悤 A T } ̊ Ă B.

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V A { J X N { C X g j O ̕ @ ܂ IWEB łł 閳 ̃{ C X g j O I т̒ ֌W Ă т̒ d Ȃǂ́A l ꂼ ꌈ ܂ Ă ܂ B ɒ 邱 Ƃ͏o ܂ ̂ŁA o ቹ ɂ͌ E ܂ B g j O ς ł A o ቹ ̂ł g 悤 Ȑ ɂ Ă A Ⴂ ꂢ ɋ 悤 ɂ 邱 Ƃ͏o ܂ A ȏ ͒ቹ ̉ L ΂ Ƃ͏o ܂ B ł́A Ă 鐺 łǂ̂悤 ɒቹ o Ă ΂ A C g ܂ B. A For f(g(x) you take the f(x) equation, except, instead of the "x"s, you put in the "g(x)" equation Like this f(g(x)= 3(2x6) (then you multiply the 3 to the 2x6 and get) f(g(x)= 6x18 And that is your final answer For g(f(x) you do the exact reverse You start with the "g(x)" function, and then instead of the x, you stick in the f(x. This is written as "(f o g)(x)", which is pronounced as "fcomposeg of x" And "( f o g)(x)" means "f (g(x))" That is, you plug something in for x, then you plug that value into g, simplify, and then plug the result into f The process here is just like what we saw on the previous page, except that now we will be using formulas to find values.

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C x g ԌߑO11 ` ߌ R a ` q @ c t e h X y C 780 ~ ۂ̓ w G o 10. (h@g)(x)= 16x^28x1 For ease of visualisation set g(x)=y=4x1 So h(y)=y^22 but y=4x1 so by substitution we have (h@g)(x)= (4x1)^22 (h@g)(x)= (16x^28x1)2 (h@g)(x)= 16x^28x1. Simple and best practice solution for g=(xc)/x equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Solution for If f(x) = x^22x1 and g(x) =(2x3), find each of the following functions (a) f o g (b) g o f (c) g o g o g.