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.

Question

loviy · Answer

In deriving the Inverse function of a given function, you need to switch the position of x and f(x), and isolate the f(x).

loviy · Answer

Here is an example:
$$f(x) = \frac{5x+6}{7} \  x = \frac{5f(x) + 6}{7}  $$

loviy · Answer

So, we need to get rid of the 7 that is being divided first. Hence multiply it on both sides.
$$7 * x=\frac{5f(x) + 6}{7} * 7 \ 7x = 5f(x) + 6$$

loviy · Answer

Then, we need to get rid of 6, so subtract it on both sides.
$$7x - 6 = 5f(x) + 6 - 6 \7x - 6 = 5f(x) \  \text{Divide both sides by 5} \ \frac{7x - 6}{5} = \frac{5f(x)}{5} \  \frac{7x - 6}{5} = f(x) \  \text{OR}  \   f(x) = \frac{7x - 6}{5}$$

loviy · Answer

After that, you will be able to use the given x..
Pleasure to help you! God bless!