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One-to-one function: A function is called one-to-one if not any two values of x produce the same y. Mathematically specking, this is the same as saying,
f ( x1 ) ≠ f ( x2 )
whenever x1 ≠ x2
Thus, a function is one-to-one if whenever we plug distinct values into the function we get different function values. Sometimes it is simpler to understand this definition if we illustrates a function that isn't one-to-one.
Let's take a look at 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 different values of x that generate the same value of y. Note down that we can turn f ( x ) = x2 into a one-to-one function if we limit ourselves to 0 ≤ x <∞ . It can sometimes be done with functions.
Illustrating that a function is one-to-one is frequently tedious and/or difficult. For the most part we are going to suppose that the functions which we're going to be dealing with in this course are either one-to-one or we have limited the domain of the function to get it to be a one-to-one function.
Now, let's formally define just what inverse functions are.
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
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Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.
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a triangle is 180
how do you you find 40% if you 35 out of 40
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