Ex 1-5 - e"f(l 5 c{l 6 Ifl(r =t I md 8(I = t(r l...

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1.5 Combiliag fLnctiorsi shiftirg ald Scating 6laphs 45 FIGURE 1.62 GFph ofthe ellipse - + - = l,a > D, where the mior Substinrting r , for x, and .r /. forr, in Equation (2) results in G ht'1 (v - kJ'z ; .+ - =1. (3) a' b' Equation (3) is the ltrn&rd equation ofxn ellipse with center at (1, tr). The geometric definition a.nd properties of ellipses are reviewed in Section 10.1. Sums, Differences, Products, and ouotients In Erercises I ard 2. find the domains and ranges ofl. & I + I, and r. lG)=r.8(,)=\,u 2. lG)= \4+ 1, sG)=\4 1 In Exercises 3 and 4. find the doftains and ranges of/, & l/g, and s//. 3. l(r) = 2. 8(r) = r'? + I a./(r)=1, s(r) =l+\4 Composites of Functions s. If/(r) = I + 5mds(:) = r'? 3, fid th€ following. r. .f(c(0.)) c. "f(c(r))
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Unformatted text preview: e. "f(l( 5) c. .{l(}) 6. Ifl(r) =t I md 8(I) = t/(r + l), fildthe followins. 7. If&(r) : ar - 5, v(x) = r':. and /(r) = l/,, find tomulas fo. b.,(/(!(r))) d. r(l(,G))) r l/(!(r))) s.It [email protected] = "4,sG) = tl4, ed n(a) = 4r - 8, find fomulas ^. u(!(l1\) c. !(!UG))) a.f(r(rc))) ^. [email protected])) c. s(h(JGD) .. IG(h(t))) b. rok(r)) d. s0(r(r))) r' Ih([email protected])) b. c0(o)) d. sUG)) t' BGQ)) h.8GG)) t\ sU(1/2\) d. cUG)) r' eGQ)) h.8G(r)) Let l(') = , - 3. 8(x) =\4. t(,) :'r,aidj(r) :21.Ex-press each ofthe ftnction! in Exercises 9 md l0 as a composite h-volvins one or more of/. & n, andj. ,. JG(t/2)) c. ,fk(')) e. fcQ)) c. ,r0(') s.a.t="4-t- /-:-i e. t= v(r rf 10.!. l=2t 3 e' 1':zlG-: b, r = 2\/t t t,=(2r 6f t, y:'rF -3...
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