Question

The function f(x) =5x coverts x nickels to pennies. Find a function that converts X Pennys to Nichols then convert 50 pennies to Nichols. 

Answer 1

`f'(x) = (1)/(5)x`

Explanation:

Given

`f(x) = 5x` --- 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:

`f(x) = 5x`

Represent f(x) with y

`y = 5x`

Swap the positions of x and y

`x = 5y`

Make y the subject by dividing both sides by 5

`(1)/(5)x = (5y)/(5)`

`(1)/(5)x = y`

`y =(1)/(5)x`

Replace y with f'(x)

`f'(x) = (1)/(5)x`

Hence, the function that converts x pennies to nickels is
`f'(x) = (1)/(5)x`