# Evaluate g 3 g 3 3 1 g 3 4 f 3 g 3 2 4 fg 3 12

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Evaluate g (-3)g (-3) = (-3)-1 => g (-3) = -4f (-3) / g (-3) => 2/-4 f/g (-3) =-1/2Explanation for part (b):(a)Since there are no variables in the expression, the domain is all real numbers. {x| x є }23Answers:(a)2√26 10.19803902(b)(8, -1)(c)(8, 1)Work for part (a): find diameter using the distance formula d = √(x2– x1)2+ (y2– y1)2d = √ ((9) – (7))2+ ((4) – (6))2=> d = √ (9 – 7)2+ (4 – 6)2d = √ 22+ 102 => d = √4+ 100 => d = √104 => √4(26)d = 2√26 10.19803902Work for part (b):Find center point using formula C= ( (x1+ x2) / 2,(y1+ y2) / 2 )C=+9/2, -6+4/2 => 16/2 , -2/2C= (8, -1)
Math 107 Final ExaminationSpring, 20174Work for part ( c): The point symmetric to the y-axis has the y-coordinate change in sign. So, that point would be (8, 1)24Answer: y = -5x+17Work: y = mx+bm= -3-(7) / 4-(2) => m= -10 /4-(2) => m=-10/2 => m = -5y= (-5). x+ b => y= (-5). (2) +b(7) = (-5). (2) +b => (-5). (2) +b =7 => -10 +b =7 => b = 17Y= -5x +1725Answer: \$39300Work: Commission= Paycheck-salary4379.40 - 2100 = 2279.40Amount of sales =commission / percentage2279.40*100/5.8Sales=39300 26Answers:(a)2x2- 12x + 11(b)6+√2(7+x)/2, 6 - √2(7+x) /2Work for part (a) and for part (b):a)f(x-3) = 2(x-3)2-7=>2((x-3) (x-3))-7 => 2(x2- 6x + 9) -7=>2x2-12x+18-7 => 2x2-12x+11b)(2x2-12x+11) => y= 2x2-12x+11=> 12±√ (-12)2– 4. (2. (11-x)) /2. 2 => 12±√ 144 – 4. (2. (11-x)) /2. 2=>12±√144– 4 (22-2x) /2. 2 =>12±√56+8x /2. 2=> y = 12±√8(7+x) /2. 2 => y = 12± 2√2(7+x) /2. 2
Math 107 Final ExaminationSpring, 20175=> y = 12± 2√2(7+x) /4 => y = 6± √2(7+x) /2=> (f0g)(-1)= 6+√2(7+x) /2, 6 - √2(7+x) /227Answer: x= 4+√13/3, 4-√13 / 3 Work:3x2+1-8x=08±√ (-8)²-4. (3 .1) / 2 .3 => 8±√ 64 – 4. 3 / 2 .3=> 8±√ 64-12 / 2.3=> 8±√52 / 2.3=>8±√22.13/ 2.3 => 8±2√13/ 2.3 => 8±2√13/ 6=> x= 4±√13/ 3 => x= 4+√13/ 3, 4-√13/ 328Answer: f-1(x)=5x+30Work:Replace f(x) with y1/5x-6 => x = 1/5 y – 61/5. Y /1-6=x=> y/5 - 6 = x => y = 6. (5) +x. (5) => y= 30+5x => y = 5x+30f-1(x) = 5x + 3029Answers: P(x) = –0.001x2+ 3.2x – 1550a)520b)1600Work for (a):P= -0.001. 9002 + 3.2 (900) – 1550P= -0.001. 810000 +3.2(900) – 1550P= -810 + 3.2(900) – 1550P= -810 + 2880 – 1550P= 2070 -1550P= 520Work for (b):-b/2a-4.2 / 2. -0.001-4.2 / -0.002
Math 107 Final ExaminationSpring, 20176160030Answer: x+1/x3Work: x +7/x+3 + 24/(x+3) (x-3)=>x+7/x+3 x-3/x-3 + 24/ (x-3) (x-3) => (x+7) (x-3) +24 / (x+3) (x-3)=>x²+4x-21+24 / (x+3) (x-3) => x²+4x+3/ (x+3) (x-3)=>(x+1) (x+3) /(x+3) (x-3)=> x+1 / x-3
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