Question

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)

Answer 1

Given that:

The function to represent the growth of Neveah hair is

`f(x)=(2x+4)/(3)`

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,

`f(x)=(2x+4)/(3)`

Put f(x)=y.

`y=(2x+4)/(3)`

Interchange x and y.

`x=(2y+4)/(3)`

Isolate y.

`3x=2y+4`

`3x-4=2y`

`(3x-4)/(2)=y`

Put
`y=f^(-1)(x)`.

`f^(-1)(x)=(3x-4)/(2)`

So, the required inverse function is
`f^(-1)(x)=(3x-4)/(2)`. 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.

`f^(-1)(6)=(3(6)-4)/(2)`

`f^(-1)(6)=(18-4)/(2)`

`f^(-1)(6)=(14)/(2)`

`f^(-1)(6)=7`

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