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

Answer:

$f'(x) = \frac{1}{5}x$

Step-by-step 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

$\frac{1}{5}x = \frac{5y}{5}$

$\frac{1}{5}x = y$

$y =\frac{1}{5}x$

Replace y with f'(x)

$f'(x) = \frac{1}{5}x$

Hence, the function that converts x pennies to nickels is $f'(x) = \frac{1}{5}x$