Question

If f(x) = 5x, what is f–1(x)?

Answer 1

Answer: x/5

================================

Step-by-step explanation:

Think of f(x) = 5x as y = 5x
The idea is to swap x and y, and then solve for y

y = 5x
x = 5y
5y = x
5y/5 = x/5
y = x/5

Making the inverse function
`f^(-1)(x) = (x)/(5)`

In simpler terms, we're basically undoing what we do to x originally. We multiplied x by 5, so the inverse will undo that and divide x by 5

Example:
Take the value x = 10 and plug it into the function to get
f(x) = 5*x
f(10) = 5*10
f(10) = 50
So the output is 50
If we take that output and plug it into the inverse g(x) we get
g(x) = x/5
g(50) = 50/5
g(50) = 10
which is the original input