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Maths

 

27th August, 2021

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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1.). No.

2.). Yes

3.). No.

4.). Yes

5.). Ans :x2 +y2= 16

6.). Ans : (x+8)2 +(y-6)2 =100

7.). Ans : (x+6)2 +(y+8)2 =100

8.). Ans : (x-5)2 +(y+4)2 =6

9.). Ans : (x +2)2 +y2 =4

10.). Answer : in graphing the circle, the center is (0,0), radius, r =9

The domain is [-9,9]

The range is [-9,9]

NOTE; kindly use the graphing calculator ( link provided below), by inserting equation of the circle you will be able to see the circle graph , then use the graphing tool ( in the online class ) to draw a circle exactly same as the one displayed in graphing calculator.

Graphing calculator (https://www.desmos.com/calculator

IMG_2293

11.) Answer : in graphing the circle, the center is (2,3), radius, r =4

The domain is [-2,6]

The range is [-1,7]

12.).Answer : in graphing the circle, the center is (-6,1), radius, r =5

The domain is [-11,-1]

The range is [-4,6]

13.).Answer : in graphing the circle, the center is (-2,-3), radius, r =2

The domain is [-4,0]

The range is [-5,-1]

14.).Answer : in graphing the circle, the center is (0,1), radius, r =7

The domain is [-7,7]

The range is [-6,8]

15).Answer : in graphing the circle, the center is (-1,0), radius, r =6

The domain is [-7,5]

The range is [-6,6]

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16.). (x+2)2 +(y+1)2 =1

17.). (x-3)2 +(y-4)2 =1

18.). (x +2)2 + (y-2)2 = 9

19.). (x – 4)2 + y2 =25

20.).) Ans: 20π

 

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15.). a.) f-1 (x) = (∛x) -3

b.). Graph D

c.). Domain of f-1 (x) = (-∞, ∞)

Range of f-1 (x) = (-∞, ∞)

16.). a.) f-1 (x) = x2 +12 ;x≥12

b.). Graph B

c.). Domain of f-1 (x) = (0, ∞)

Range of f-1 (x) = (12, ∞)

17.). a.) f-1 (x) = x3 -18×2 + 108x- 216

b.). Graph B

c.). Domain of f-1 (x) = (-∞, ∞)

Range of f-1 (x) = (-∞, ∞)

18.). Ans; f(g(7)) =7

19.). Ans; (gof)(-3)) = -3

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20.). Ans; f-1 (g(9)) =3

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12.). a.) f-1 (x) = (x+5)

b.). Graph A

c.). Domain of f-1 (x) = [-5, ∞)

Range of f-1 (x) = [0, ∞)

 

13.). a.) f-1 (x) = 8-(x) ;x≥0

b.). Graph B

c.). Domain of f-1 (x) = [0, ∞)

Range of f-1 (x) = (-∞,8]

 

14.). a.) f-1 (x) = ∛(x+12)

b.). Graph B

c.). Domain of f-1 (x) = (-∞, ∞)

Range of f-1 (x) = (-∞, ∞)

b.). Graph D

c.). The domain of f(x) = (-∞, ∞) and the range of f (x) = (-∞, ∞)

The domain of f-1 (x) = (-∞, ∞) and the range of f-1 (x) = (-∞, ∞)