Neveah has created the function of f(x) = 2x+4/3 to represent the growth of her hair, where x represents the number of months since her last haircut. Neveah discovers that, using inverse function to solve for X=6, she can predict when her hair will have grown 6". Explain to Neveah how to accomplish this using complete sentences.
Accepted Solution
A:
f(x)=2x+4/3
Replace f(x) by y: y=2x+4/3
Solving for x: y-4/3=2x+4/3-4/3
Subtracting the two terms on the left side of the equation: (3y-4)/3=2x
Dividing both sides of the equation by 2: [(3y-4)/3]/2=2x/2 [(3y-4)/3]*(1/2)=x [(3y-4)*1]/[(3)*(2)]=x (3y-4)/6=x x=(3y-4)/6
Replace "x" by "f^(-1) (x)" (inverse function) and "y" by "x": f^(-1) (x) = (3x-4)/6 Inverse function