Question

Can someone please help me with this?

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.

Answer 1

Is f(x) = (2x + 4) / 3 or 2x + 4/3 ?

Answer 2

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

Answer 3

f(x) = (2x + 4) / 3
Find the inverse function.
Step 1: Rewrite the equation, by using y in the place of f(x):
y = (2x + 4) / 3
Step 2: To find the inverse function, switch x and y. That is put x in the place of y and y in the place of x:
x = (2y + 4) / 3
Step 3: Solve for y:
x = (2y + 4) / 3
multiply both sides by 3
3x = 2y + 4
subtract 4
3x - 4 = 2y
divide by 2
(3x - 4) / 2 = y
The inverse function is: f^-1(x) = (3x - 4) / 2

Answer 4

To find out how many months it will take for her hair to grow 6 inches, put x = 6 in the inverse function:
( 3 * 6 - 4 ) / 2 = (18 - 4) / 2 = 14 / 2 = 7 months.

Answer 5

Okay, thank you so much for clearing this up for me. You've been a big help.

Answer 6

You are welcome.