if f(x)=(-2)/3x +4, what would the inverse be? What would be the slope and the inverse of the inverse be? 

Expert Answers
jeew-m eNotes educator| Certified Educator

f(x)=(-2)/3x +4

   y =(-2)/3x +4

In this equation y is the dependant variable and x is the independent. In the inverse function y of the above function will become the independant variable and x will be the dependant. So the inverse function is something like x = f(y)

y =(-2)/3x +4

y-4 = (-2)/3x

3(y-4)/(-2) = x


x = (-3/2)y+6

So this is the inverse function. But in standard notation we keep a function as y = f(x). So if we interchange x and y the inverse function will be;

y = (-3/2)x+6


The gradient of the inverse function is (-3/2).


Inverse of a inverse function gives the original function. So inverse of the inverse will be;

y =(-2)/3x +4