Inverse of f(x): Is it a Function or Relation?

AI Thread Summary
To find the inverse of the function f(x) = (x-4)/3, the correct inverse is f^-1(x) = 3x + 12, not 3x + 4. The discussion highlights the importance of letting y = f(x) and solving for x to derive the inverse. Additionally, it emphasizes the need to verify the inverse by substituting test values to ensure accuracy. The inverse function is confirmed to be a function, as it passes the vertical line test.
Monocerotis
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Homework Statement



Find the inverse of each function. Is the inverse a function or a relation ?

f(x) = (x-4)/3



The Attempt at a Solution


Not sure which one is correct, and if any are not sure why (as in rules that may apply)

f(x) = (x-4)/3
f^-1(x) = 3x+4

or

f^-1 3x+12
 
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A way I usually approach such questions is by letting y = f(x), then making x the subject. Clearly then, the expression (in y) will give the inverse function.

Another way would be by observing that
f^{-1} (\frac{x - 4}{3}) = x = (\frac{x - 4}{3}) (3) + 4

You can always check the validity of your function by substituting test values.
 

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