Question

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.

Answer 1

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