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 si nce 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.
1 answer:
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
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