Chapter 1 Solutions cont.

# Chapter 1 Solutions cont. - Section 1.5 Combining Functions...

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Section 1.5 Combining Functions; Shifting and Scaling Graphs 27 3. D : x , D : x D : x since g(x) 0 for any x; D : x fg f g g f ±_² ²_ ±_² ²_ Ê Á Î Î since f(x) 0 for any x. R : y 2, R : y 1, R : 0 y 2, R : y Áœ   ² Ÿ   fgf g Î gf Î " # 4. D : x , D : x 0 D : x 0 since g(x) 0 for any x 0; D : x 0 since f(x) 0 f g g f ±_ ² ² _   Ê   Á     Á ÎÎ for any x 0. R : y 1, R : y 1, R : 0 y 1, R : y  œ ² Ÿ   " g Î Î 5. (a) f(g(0)) f( 3) 2 œ±œ (b) g(f(0)) g(5) 22 œœ (c) f(g(x)) f(x 3) x 3 5 x 2 œ± œ ± ³ œ ³ ## # (d) g(f(x)) g(x 5) (x 5) 3 x 10x 22 œ ³œ³ ±œ³ ³ (e) f(f( 5)) f(0) 5 ±œ œ (f) g(g(2)) g(1) 2 ± (g) f(f(x)) f(x 5) (x 5) 5 x 10 œ ³œ³³œ³ (h) g(g(x)) g(x 3) (x 3) 3 x 6x 6 œ ± ± œ ± ³ # % # 6. (a) f g f ˆ‰ ˆ "" # ± 2 33 (b) g f g 2 ˆ‰ˆ (c) f(g(x)) f 1 ± œ ± ²² ² x1 x (d) g(f(x)) g(x 1) œ œ ±² (x 1) 1 x (e) f(f(2)) f(1) 0 (f) g(g(2)) g œ 34 3 4 3 (g) f(f(x)) f(x 1) (x 1) 1 x 2 œ ±œ±±œ± (h) g(g(x)) g (x 1 and x 2) œ Á ± Á ± ² " # ² x 1 x " 7. (a) u(v(f(x))) u v u 4 5 5 œ ± œ ± ‰ˆ " # xxx x 4 (b) u(f(v(x))) u f x u 4 5 5 œ ± œ ± ab # xx x 4 # (c) v(u(f(x))) v u v 4 5 5 ±

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Chapter 1 Solutions cont. - Section 1.5 Combining Functions...

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