Inverse

F(x) = 2x+3.. Find F(F^-1(-5))

We need to find the inverse......Let's write this as :

y = 2x + 3      get x by itself

y - 3 = 2x      divide by 2 on both sides

[ y - 3 ] / 2 =  x    "exchange" x and y

[x - 3 ] / 2 = y    and for y, we can write :

[x - 3 ]  / 2  = F^-1(x)

So  F^-1(-5)  =   [ - 5 - 3 ] / 2 =   -8 / 2  = -4

And F (F^-1(-5))  = F(-4)  =  2(-4) + 3 = -5

Notice something odd......the result of this is that the F and F^-1 seemingly "cancel" each other and we're just left with the -5  !!!!!

In actuality......the result of F^-1(-5)   would lead us back to the original value for "x" that we put into F - in this case, 4 - and this returns the " -5"  when we evalate F(4)