SOLUTION: I am having a hard time understanding what inverse functions are and how you figure out what the inverse is of a given function. Can someone please explain?! I'm also trying to so

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I am having a hard time understanding what inverse functions are and how you figure out what the inverse is of a given function. Can someone please explain?! I'm also trying to so      Log On


   



Question 324950: I am having a hard time understanding what inverse functions are and how you figure out what the inverse is of a given function. Can someone please explain?!
I'm also trying to solve: What is the formula of the inverse function of y= 4^-2X?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Functions give you a certain output for given input.
What if I found a function that if I stuck in the output, it would give me the original input.
That's what an inverse function does.
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In other words, say
f%283%29=15
If I found a function would use the 15 value to give you 3.
g%2815%29=3
Then g(x) would be the inverse of f(x) (as long as it worked for every other x value too)
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As an example of simple linear functions,
f%28x%29=2x%2B5 and g%28x%29=%28x-5%29%2F2 are inverse functions.
Try it and see.
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Now to your example, exponential functions and logarithmic functions are inverses of each other.
y=4%5E%28-2x%29
Here's how you find an inverse funtion.
Start with your function.
y=4%5E%28-2x%29
Interchange positions of x and y.
highlight%28x%29=4%5E%28-2%2Ahighlight%28y%29%29
Now solve for y.
That new y will be the inverse function of the original function f%28x%29, symbolically f%5E%28-1%29%28x%29.
log%284%2C%28x%29%29=-2y
y=-%281%2F2%29log%284%2C%28x%29%29%29+
highlight%28f%5E%28-1%29%28x%29=-%281%2F2%29log%284%2C%28x%29%29%29%29+