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

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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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

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