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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.
Find the length of the second diagonal of a rhombus, whose side is 5cm and one of the diagonals is 6cm.
HE IGHTS AND DISTANCES If the angle of elevation of cloud from a point 'h' meters above a lake is α and the angle of depression of its reflection in the lake is β , prove
Bill traveled 117 miles in 2.25 hours. What was his average speed? Use the formula d = rt (distance = rate × time). Substitute 117 miles for d. Substitute 2.25 hours for t and
The angle calculate of the base angles of an isosceles triangle are shown by x and the vertex angle is 3x + 10. Determine the measure of a base angle. a. 112° b. 42.5° c.
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In this section we will be looking exclusively at linear second order differential equations. The most common linear second order differential equation is in the type. p (t ) y
(6x+9y) + (11x+13y)
online Exam
1/cos(x-a)cos(x-b)
The length of the diameter of the circle which touches the X axis at the point (1,0) and passes through the point (2,3) is ? Solution) If a circle touches the x-axis, its equatio
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