Answer:
[tex]f'(x) = \frac{1}{5}x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x[/tex] --- Nickel to Penny
Required
Determine the function that converts penny to nickel
This question implies that we determine the inverse of the function.
We have:
[tex]f(x) = 5x[/tex]
Represent f(x) with y
[tex]y = 5x[/tex]
Swap the positions of x and y
[tex]x = 5y[/tex]
Make y the subject by dividing both sides by 5
[tex]\frac{1}{5}x = \frac{5y}{5}[/tex]
[tex]\frac{1}{5}x = y[/tex]
[tex]y =\frac{1}{5}x[/tex]
Replace y with f'(x)
[tex]f'(x) = \frac{1}{5}x[/tex]
Hence, the function that converts x pennies to nickels is [tex]f'(x) = \frac{1}{5}x[/tex]
