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.

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

Then, for x=6

f^ (-1) (6) = [ 3 (6) - 4]/6

f^ (-1) (6) = (18-4) / 6

f^ (-1) (6) = 14/6

f^ (-1) (6) = 7/3

Her hair will have grown 6 after 7/3 = 2.33 months