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why x=y2-5y is not a function but y x2-5 is

Mathematics
Tutor: None Selected Time limit: 1 Day

So the question is asking why x=y2-5y is not a function but x=y2-5y is not. The question also says to substitute -6 with x to solve for 1. (the 2 is an exponent just so you know). I solved y=66 in the first one, but got -1 for the second...??

Sep 8th, 2014

1)   x = y^2 - 5y  ,  x = - 6

  - 6 = y^2 - 5y

 y^2 - 5y + 6 = 0

(y - 2)(y - 3) = 0  ,  factorise

y-2 = 0 or  y - 3 = 0 

 y = 2  , y = 3

( -6 , 2 ) & ( -6 , 3 ) are the points 

- 6 has two images 2 & 3

not a function as x cannot have two different images

2)   y = x^2 - 5

 x = - 1

  y = ( - 1)^2 - 5

   y = 1 - 5 = - 4

  (- 1 , - 4 )

- 1 has only one image so it's a function 

Sep 8th, 2014

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