Can someone explain step by step how f^-1(x) is the inverse of f(x)
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Can someone explain step by step how f^-1(x) is the inverse of f(x)

[From: ] [author: ] [Date: 13-09-28] [Hit: ]
Example 2: if f(x) = e^x, the inverse is ln(x).Example 3: if f(x) = 3x - 5,Example 4: if f(x) = 17 - x, the inverse is 17 - x.Does that look weird?......
Something raised to the power of -1 is like this:
x ^ -1 = 1 / x
Does that help?

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f^(-1) (x) is just a NOTATION for the "inverse" of f(x).

The "inverse" of a function intuitively means a function that "undoes" the operation of the original function.
For example if f(x) = x^2, the inverse is sqrt(x).
Example 2: if f(x) = e^x, the inverse is ln(x).
Example 3: if f(x) = 3x - 5, the inverse is (x+5)/3
Example 4: if f(x) = 17 - x, the inverse is 17 - x.
Does that look weird? Well, here's the thing: if you subtract a number from 17, and then you go and subtract the RESULT from 17, it gets you back to the original number, right? Similarly:
Example 5: If f(x) = 3/x, the inverse is 3/x. Same reasoning as example 4.
Example 6: If f(x) = 5^x, the inverse is log(x)/log(5).
Example 7: If f(x) = 1/(x-2) the inverse is (2x+1)/x.
To see this one, let's say the original x is 7. Then f(x) is 1/5. Now apply the "inverse" to the 1/5, and you get (1.4)/(0.2) = 7...exactly what you started with.

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chill out bro f^-1(x) is the notation used to denote inverse of f(x).. no step by step explanation needed its just a notation ...
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