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alexira [117]
3 years ago
10

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 repre

sents 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)
Mathematics
1 answer:
dangina [55]3 years ago
3 0

Given that:

The function to represent the growth of Neveah hair is

f(x)=\dfrac{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)=\dfrac{2x+4}{3}

Put f(x)=y.

y=\dfrac{2x+4}{3}

Interchange x and y.

x=\dfrac{2y+4}{3}

Isolate y.

3x=2y+4

3x-4=2y

\dfrac{3x-4}{2}=y

Put y=f^{-1}(x).

f^{-1}(x)=\dfrac{3x-4}{2}

So, the required inverse function is f^{-1}(x)=\dfrac{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)=\dfrac{3(6)-4}{2}

f^{-1}(6)=\dfrac{18-4}{2}

f^{-1}(6)=\dfrac{14}{2}

f^{-1}(6)=7

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

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