F(x)= (x-c)/(x-3). Given there is only one value of x that maps onto itself under function f,find value of c.

So you know that f(x)=x for only one value of x.





Solving f(x) = x


x = (x-c)/(x-3)


x(x-3) = x-c


x^2-3x = x-c


x^2 - 4x + c = 0





So you know that this quadratic has only one real root. Look at the discriminant (ie if you had ax^2+bx+c the discriminant would be b^2 - 4ac). For only one real root you need discriminant equals zero, so here we have


(-4)^2 - (4 x 1 x c) = 0


16 - 4c = 0


so c = 4.





Hope this helps you!

F(x)= (x-c)/(x-3). Given there is only one value of x that maps onto itself under function f,find value of c.
let y represent f(x)





y=(x-c)/(x-3)





y(x-3)=x-c





y(x-3)-x=-c





c = -y(x-3)+x





I believe that should be the answer or your doorway to the answer.. *crosses fingers* good luck!
Reply:I agree with Jess and you can check it is correct since in





y = (x - 4)/(x - 3) when x = 2 you get y = -2/-1 = 2