Functions help

Question

determine whether F(x)=2x-6 is a one to one function

Answer 1

To test the one to one property of a function.

  can graph the function and draw a horizontal and a vertical lines.

  If the vertical and Horizontal lines intersect the graph in one and only one point, then the function is one to one.

 

   F( X ) = 2X - 6

 

     Y = 2X -6 

 

    Let's find F( a), value of f( x ) for X=a

 

     F( a ) = 2a -6 

 

   Now : lets find X for F(x) = F( a)

 

    F(a) +6 = 2X

 

    X = ( F(a)+ 6 / 2

 

     We see that for any value of X there is one and only one value of F(x), and for any value of F(x) there is only one value of X.

 

  Therefor Function is one-to- one.