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  3. A practical way to determine this is through the horizontal line test: if any horizontal line intersects the graph of the function at most once, the function passes the test and has an inverse.
    www.storyofmathematics.com/how-to-tell-if-a-functi…

    To verify the accuracy of the inverse:

    • Pick a point \ ( (a,b)\) on the original function’s graph.
    • Check that the point \ ( (b,a)\) exists on the graph of the inverse function.
    www.effortlessmath.com/math-topics/how-to-grap…
    To check whether a function (f (x)) has an inverse, I always ensure that it’s a one-to-one function, meaning it passes both the vertical and horizontal line tests. When I find the inverse of a function, I swap the roles of (x) and (y) and then solve for the new (y), which is the inverse function.
    www.storyofmathematics.com/how-to-write-an-inve…
    Once the inverse is found, I like to verify it by checking two main properties: whether the inverse function is indeed a function and if the composition of the original function and its inverse yields the identity function. For instance, f (f − 1 (x)) = x and f − 1 (f (x)) = x.
    www.storyofmathematics.com/how-to-find-inverse-f…
    Checking inverse of f: X → Y Step 1 : Calculate g: Y → X Step 2 : Prove gof = I X Step 3 : Prove fog = I Y g is the inverse of f
    www.teachoo.com/7100/1166/How-to-check-if-funct…
     
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    WEBLearn how to verify if two functions are inverses of each other using function composition. See examples, diagrams and steps to prove or disprove the inverseness of functions.

     
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    WEBVerify inverse functions. Determine the domain and range of an inverse function, and restrict the domain of a function to make it one-to-one. Find or evaluate the inverse of a function. Use the graph of a one-to-one …

  14. Inverse function - Math.net

    WEBLearn how to find the inverse of a function by doing the opposite of what the original function does to x. See examples, rules, and graphs of inverse functions and their reflections.

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    WEBLearn how to check if two functions are inverses of each other by using the composite functions. See examples and practice problems on verifying inverse functions in precalculus.

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