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1)This circle passes through the points (-1, 2),(3,0)  and (9,0). The center of the circle is at (h, k). What is the value of h+k? 

2)The values of a function f(x) are given below:

Evaluate f^{-1}\left(f^{-1}(50)\times f^{-1}(10)+f^{-1}(26)\right)

 Dec 27, 2019
edited by BIGChungus  Dec 27, 2019
 #1
avatar+106516 
+2

1)  

We have these equations

 

(-1 -h)^2  + (2 - k)^2  = r^2

(3 - h)^2  + k^2  = r^2

(9 - h)^2  + k^2  = r^2

 

Subtract the  second equation from  the 3rd and we have that

 

(9 - h)^2  - (3 - h)^2  =  0    simplify

 

h^2 - 18h  + 81  -  [ h^2 - 6h  + 9  ]  = 0

 

-12h  + 72   =0

 

-12h  = -72

 

h = 6

 

And  equating the first two equations

 

(-1 - 6)^2  + (2 - k)^2  =  (3 - 6)^2  + k^2

 

49  + k^2 - 4k + 4  =  9  + k^2

 

53  - 4k  =  9

 

44 - 4k  = 0

 

k  = 11

 

So

 

(h, k) =  (6, 11)

 

And  h + k  =  17

 

 

cool cool cool

 Dec 27, 2019
 #2
avatar+106516 
+2

2)

 

\( f^{-1}\left(f^{-1}(50)\times f^{-1}(10)+f^{-1}(26)\right) \)

 

f-1 (50)  =  7

f-1 (10)  = 3

f-1  (26)   =  5

 

So   we are evaluating this

 

f-1  (  7  x 3  +  5)  =

 

f-1  ( 21  + 5)  =

 

f-1 (26)  =

 

5

 

 

cool cool cool

 Dec 27, 2019

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