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A function is called one-to-one if no two values of x produce the same y. It is a fairly simple definition of one-to-one although it takes an instance of a function which isn't one-to-one to illustrate just what it means. However Before doing that we have to note that this definition of one-to-one is not actually the mathematically correct definition of one-to-one. This is similar to the mathematically correct definition it just doesn't employ the entire notation from the formal definition.
Now, let's look at an example of a function which isn't one-to-one. The function f ( x )= x2 is not one-to-one since both f ( -2) = 4 and f ( 2) = 4 . In other terms there are two distinct values of x which produce the similar value of y. Note that we can turn f ( x ) = x2 into a one-to-one function if we limit ourselves to 0 ≤ x <∞ . Sometimes it can be done with functions.
Illustrating that a function is one-to-one is frequently a tedious and often difficult. For the most of the part we are going to suppose that the functions which we're going to be dealing along with in this section are one- to-one. We did have to talk regarding one-to-one functions though since only one-to-one functions can be inverse functions.
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Simpler method Let's begin by looking at the simpler method. This method will employ the following fact about exponential functions. If b x = b y then x
Domain and Range The domain of any equation is the set of all x's which we can plug in the equation & get back a real number for y. The range of any equation is the set of all
Example Find out all the zeroes of P ( x ) = x 4 - 7 x 3 + 17 x 2 -17 x + 6 . Solution We found the list of all possible rational zeroes in the earlier example. Follo
how to to a equations ?
The national demand and price for a certain type of energy-efficient exhaust fan are related by p=490-4/5q, where p is the price(in dollars) and q is the demand (in thousands). The
1/2x-2y=4 to slope intercept form
[-(y4-y2 + 1)-(y4+2y2 + 1]+(4y4-10y2-3)
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