Find a domain on which f is one to one

One-to-One Functions

find a domain on which f is one to one

Pre-Calculus - Determine if a function is one to one

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So far, we have been able to find the inverse functions of cubic functions without having to restrict their domains. However, as we know, not all cubic polynomials are one-to-one. Some functions that are not one-to-one may have their domain restricted so that they are one-to-one, but only over that domain. The function over the restricted domain would then have an inverse function. Since quadratic functions are not one-to-one, we must restrict their domain in order to find their inverses. If a function is not one-to-one, it cannot have an inverse. If we restrict the domain of the function so that it becomes one-to-one, thus creating a new function, this new function will have an inverse.

Finding the Inverse of a Function page 4 of 7. You'll notice that the only difference between this and the previous example is that the domain has been restricted to the positive x -axis this time. Here's the graph:. Since this passes the Horizontal Line Test, I know that its inverse will be a function. And since this graph is different from that of the previous function, I know that the inverse must be different. Again, it is very helpful to first find the domains and ranges.

A function f is 1 -to- 1 if no two elements in the domain of f correspond to the same element in the range of f. In other words, each x in the domain has exactly one image in the range. And, no y in the range is the image of more than one x in the domain. If the graph of a function f is known, it is easy to determine if the function is 1 -to- 1. Use the Horizontal Line Test.

You can always find the inverse of a one-to-one function without restricting the domain of the function. Recall that a function is a rule that links an element in the domain to just one number in the range. You could have points 3, 7 , 8, 7 and 14,7 on the graph of a function.
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1.7 - Inverse Functions

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5 COMMENTS

  1. Dusursuppgo says:

    The inverse of the function f is denoted by f -1 if your browser doesn't support superscripts, that is looks like f with an exponent of -1 and is pronounced "f inverse".

  2. Chantal L. says:







  3. Eco M. says:

    Restrict the domain to find the inverse of a polynomial function | College Algebra

  4. Restikudo says:

    Fiona apple why try to change me now lyrics you re welcome from moana

  5. Aloin B. says:

    Restrict the domain to find the inverse of a polynomial function

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