Neveah has created the function f(x) =the quantity of 2x plus 4, divided by 3 to represent the growth of her hair, where x represents the number of months since her last hair cut. Neveah discovers that, using the inverse function to solve for x = 6, she can predict when her hair will have grown 6 inches. Explain to Neveah how to accomplish this, using complete sentences. (10 points)

Given that:

The function to represent the growth of Neveah hair is

where,  x represents the number of months since her last hair cut.

To find:

The inverse of function and time when her hair will have grown 6 inches.

Solution:

We have,

Put f(x)=y.

Interchange x and y.

Isolate y.

Put .

So, the required inverse function is . It represents the number of months to grow her hair x inches.

She can predict when her hair will have grown 6 inches by putting x=6 in the inverse function.

Put x=6 in the inverse function.

Therefore, growth of her hair is 6 inches in 7 months.