Cambridge Additional Mathematics

Answers 461 8 f¡^1 (x)=^1 x andf(x)=^1 x ) f=f¡^1 ) fis a self-inverse function 9af¡^1 (x)=2x+2 bi(f±f¡^1 )(x)=x ii (f¡^1 ±f)(x) ...

462 Answers EXERCISE 3A.2 1ax=¡ 5 § p 2 b no real solutions c x=4§ 2 p 2 dx=8§ p 7 e x=¡ 3 § p 5 f x=2§ p 6 gx=¡ 1 § p 10 h x=¡^ ...

Answers 463 3aC b E c B dF eG fH g A h D 4a b cd 5a b cd ef 6aG bA c E dB e I fC gD h F i H EXERCISE 3D.2 1ay=(x¡1)^2 +2 by=(x+2 ...

464 Answers eiy=¡(x¡2)^2 +6 ii(2,6) iii 2 iv fiy=¡2(x+^54 )^2 +^498 ii (¡^54 ,^498 ) iii 3 iv EXERCISE 3D.3 1a(2,¡2) b (¡ 1 ,¡4) ...

Answers 465 c 5afy:¡ 106 y 615 g bfy:3 6 y 619 g cfy:¡ 136 y 637 g dfy:¡ 86 y 6494 g EXERCISE 3D.4 1acutsx-axis twice, concave u ...

466 Answers 2ax=0or 4 b x=¡^53 or 2 c x=15or¡ 4 3ax=¡^52 § p 13 2 bx=¡ 11 6 § p 145 6 4a¡ 3 <x< 7 bx 6 ¡^13 orx> 2 5a b ...

Answers 467 3a^3 ¡ p 2 7 b 6+2 p 2 7 c ¡2+ p 5 d1+ p 2 e2+2 p 6 f p 21 ¡ 2 p 3 3 g¡ 3 ¡ 2 p 2 h 3+4 p 3 13 i 4+2 p 2 j ¡ 7 ¡ 3 p ...

468 Answers 3a(2x+ 3)(2x+6) b(2x+ 4)(2x¡5) c (3x+ 2)(3x+7) d(3x+ 5)(3x¡1) e(5x+ 2)(5x¡1) f (7x¡4)(7x¡3) 4a 2 n b 10 a c 3 b d 1 ...

Answers 469 10 a 100 g bi¼ 173 g ii 300 g iii ¼ 1397 g d 20 hours c 11 a 32 amps bi 8 amps ii 2 amps d 3 seconds c 12 a i 22 ±C ...

470 Answers 15 a 80 ±C bi 40 ±C ii 20 ±C d 30 minutes c REVIEW SET 4B 1a 17 ¡ 11 p 3 b 28 2a 5+ p 3 22 b p 77 + 2 p 11 3 c 26 + ...

Answers 471 EXERCISE 5D.1 1algy=xlg 2 blgy=3lgx clgM=4lgd dlgT=xlg 5 elgy=^12 lgx flgy=lg7+xlg 3 glgS=lg9¡lgt hlgM=2+xlg 7 i lgT ...

472 Answers ciDomain is fx:x> 2 g, Range is fy:y 2 Rg iii iiVA i s x=2, x-intercept 27 , noy-intercept iv x=7 v f¡^1 (x)=52+x ...

Answers 473 2a^12 b¡^13 ca+b+1 3aln 144 bln ¡ 3 2 ¢ cln ³ 25 e ́ dln 3 4a^32 b¡ 3 c 2 x d 1 ¡x 5alg 144 blog 2 ¡ 16 9 ¢ clog 480 ...

474 Answers EXERCISE 6A.3 1aquotient isx+1, remainder is¡x¡ 4 bquotient is 3 , remainder is¡x+3 c quotient is 3 x, remainder is¡ ...

Answers 475 4aa=1, b=¡ 2 , c=3 b¢ofx^2 ¡ 2 x+3is¡ 8 ) the only real root isx=¡ 3. 5a 1 b ¡ 53 6anot a factor bfactor 7 k=6 8 a=4 ...

476 Answers 2a x^1234 ypx 9 14 19 24 bcy=5 p x+ 4 p x ,x> 0 d y=21 3a^1 x 1 0 : 5 0 : 33 0 : 25 xy ¡ 1 0 0 : 33 0 : 48 bca=1, ...

Answers 477 EXERCISE 8A 1a¼ 2 c b ¼ 3 c c ¼ 6 c d 10 ¼c e 20 ¼c f^34 ¼c g^54 ¼c h^32 ¼c i 2 ¼c j 4 ¼c k^74 ¼c l 3 ¼c m ¼ 5 c n^4 ...

478 Answers 2asinμ=§^35 b sinμ=§ p 7 4 c sinμ=0 dsinμ=§ 1 3asinμ= p 5 3 b cosμ=¡ p 21 5 c cosμ= 4 5 dsinμ=¡^1213 4atanμ=¡ 2 p^12 ...

Answers 479 REVIEW SET 8B 1a 72 ± b 225 ± c 140 ± d 330 ± 2 3acos(^32 ¼)=0, sin(^32 ¼)=¡ 1 bcos(¡¼ 2 )=0, sin(¡¼ 2 )=¡ 1 4asin(¼ ...

480 Answers b c d e f 6aa=3,b=1, c=0 ba=2,b=5, c=6 c a=5,b=3, c=¡ 2 7 m=2,n=¡ 3 8a b EXERCISE 9C 1a b c d e f g 2 -2 ¼¼ 22 ¼¼ x ...