Expert: Scott A Wilson - 2/4/2012

Question
Given f:x = 2x+p and ­­fˉ­­­­¹:x = m(4x=3), where p and m are constants. Find the value of p and value of m.

Answer
y=2x+p, x=m(4y-3)
The slope times the slope of the inverse is equal to 1.
This means that 2 * 4m = 1, so m = 1/8.

Now the equations are x = 2x + p and x = y/2 - 3/8.
To be inverses, any value must return the same value.
If x=0, y=2(0)+p=p.  Since y=p, x=m(4p-3).
Since we started with x=0 amd know m=1/9, 4p-3=0.

This says that 4p=3, so p = 3/4.

The equations can be found by putting in the values of m and p.
To do a test, try any value of x, find y, and put this in the inverse
to see if it gets back to x.  That is, test x = fˉ­­­­¹(f(x)).