Honors Pre-Calculus Practice Name: ______________________________________ Unit 1 Day 2 Compositions and Inverses of functions COMPOSITION OF FUNCTIONS GRAPHICALLY

Let f(x) = 9 – x , g(x) = x2 + x, and h(x) = x – 2. Compute the following: 11. g(f(x)) 12. (f ⃘g)(4) 13. (h ⃘g)(x) 14. g(h(f(5))) 15. h(g(f(13))) 16. f(g(h(-8)))

DE-COMPOSING FUNCTIONS: 17. Decompose: f(g(x)) = √\ − 1 18. f(g(x)) = ^_`ab. Find f(x) and g(x).

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INVERSE FUNCTIONS

19. For each relation shown: a) Is the relation a function? b) Without graphing, determine if the relation has an inverse that is a function. c) Is the relation one-to-one?

20. For each relation shown, graph the inverse.

21. Find an equation cdb(\) if c(\) = ``ab. Give the domain of cdb(\), including any restrictions “inherited” from c.

22.f(x)=3x3–5

Istheinverseafunction?

Proving Inverses by Compositions:

a yes a No a No

Ori theb Yes b Yes b No

1,1 1,17d Yes c NO c NO

2,3 13,27 o

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4,0 0,4 Domain5,3 3,5 Domain

Range Range

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NO

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g Hx 3x j 3i

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