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chapter 1 26 - 26 CHAPTER 1 FUNCTIONS AND MODELS...

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Unformatted text preview: 26 CHAPTER 1 FUNCTIONS AND MODELS 40.f(1:)=\/2_£-—+T§, D:{:c|:c2—%; g(m):x2+1. DzR. (fog)(:v):f(xz+1)=x/2(:v2+1)+ =x/2x2+5, DzR. (90f)(m ):g f((,\/2$+3))=(\/2:L'+3)2+1=(2x+3)+1:2w+4 D={z'|a:>—- (f0 f)(x) 2w+3 =2(,/ 2$+3 )+3:\/2 2m+3 +3 D= {1|x>— (gog)(m):g(:2 +1)=)2($ +1)2 +1201:4 +2cc2 -)~1)+1=x4 +2032 +2, D: R. 41- (f 0 9 0 hm?) = f(g(h($))) = f(9($ — 1)) = f(2(1‘ -1)) :2(x—1)+1:2.’I:——1 42- (f o g o h)(30) : f(g(h($))) = f(g(1 — m)) = f((1 — 90V) :2(1*w)271=2x2—4w+1 43- (f 0 g 0 h)(w) = f(g(h(92))) = f(9(w + 3)) = f((w + 3)2 + 2) :f(w2+6w+11) : ./(x2+6m+11)—1=\/x2+6x+10 44- (fogo MW) 2 “90105)” = f(9(\/—$—+§)) : f(005m) = fi 45. Letg(:1c) : 2:2 + 1 and f(a:) 2 3110. Then (f og)(m) = f(g(m))= (m2 + 1)IO=F(1:) 46. Let g(:c) = fl and f(x) = sinm. Then (f o g)(w) : f(g(a:)) = sin( (fl) = F(:I:). m2 47. Let g($) = $2 and “33) : om): mum»: fQ+4=G(x>. 48. Letg($) = as +3 and f(.’lt) : l/m. Then (f og)(m) : f(g(:c)) : 1/(x + 3) 2 C(10). 49. Letg(t) 2 cost and f(t) : x/i. Then (f o g)(t) : f(g(t)) 2 x/cost : u(t). = u(t). taut 5o. Letg(t) = tant and f(t) = 4+ Then (f o g)(t) : f(g(t)) = 1 + tam 51. Leth(ac ): 2:2 g(w)— — 3I andf(a:)— ~ 1 ‘33. Then (fogoh)(2:)— — 1 _322 — —.H(:I:) 52. Leth(m):\/E,g x)::v—1,andf(a:)=\/§.Then (f)=ogoh(:z) x/f m— :H(m). 53. Let h(m) = fl, g(a:) 2 sec .13, and f(:1:) = 364. Then (f o g o h)(w)= (sec\/_)4 — —sec4 (fl) = H(w). 54- (a) f(9(1)) : f(6) = 5 (b) 9(f(1)) = 9(3) = 2 (C) f(f(1)) = f(3) = 4 (d) 9(9(1)) = 9(5) = 3 (e) (90 f)(3) = 9(f(3)) = 9(4) = 1 (f) (f 09)(6) = f(g(6)) = f(3) = 4 55. (a) 9(2) : 5, because the point (2, 5) is on the graph of 9. Thus, f(g(2)) : f(5) = 4, because the point (5, 4) is on the graph of f. (b) 9(f(0)) = 9(0) = 3 (C) (f 0 g)(0) = f(9(0)) = f(3) = 0 (d) (g o f )(6) 2 g( f (6)) : 9(6). This value is not defined, because there is no point on the graph of 9 that has m—coordinate 6. (e) (9 o g)(—2) = 9(g(#2)) = 9(1) = 4 (f) (fOf)(4) = f(f(4)) = f9) = — ...
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