# Find a domain on which f is one to one

## One-to-One Functions

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

and for how fast can you get pregnant after birth controlSo 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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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".

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

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Restrict the domain to find the inverse of a polynomial function