Answer: x/5
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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 [tex]f^{-1}(x) = \frac{x}{5}[/tex]
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
