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Give an example of a relation that is a function but whose inverse is not a function?
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When does a relation be a function?
A function is a relation whose mapping is a bijection.
When is the inverse of a itself a function?
Since the inverse of a function is it's reflection over the line x=y, which has a slope of 1. The only way a function can be It'a own inverse is if it is a liner function whose slope is perpendicular to the line. Since a perpendicular line is any line with the negative recoprocal of the slope, any linear function whose slope is -1 will be it's own inverse. - stefanie math 7-12 teacher
What is the difference between relations and functions?
A function is a relation whose mapping is a bijection.
What is it called if any vertical line crosses the graph of a relation more than once the relation is not a function?
The Vertical Line Test An example might be x=cos(y). At any value of x between -1 a nd +1 (a vertical line on the graph) this is multivalued (and so it is called "multivalued"). The relation is a function, because given y you can calculate x. x is a function of y. The relation between y and x can also be written y=cos-1(x) "y is the angle whose cosine is x". From that point of view you can say " y is not a function of x" because for each x, there is more than one y that satisfyies the equation. To summarize, in this example x is a function of y but y is not a function of x.
Find the function whose inverse is the same as the function itself?
f ( x ) = (x-2)/(x-1)if y = (x-2)/(x-1)yx-y= x - 2yx-x= -2+yx(y-1)=y-2x = (y-2)/(y-1)so g ( x ) the inverse function is also (x-2)/(x-1)
When does a relation be a function?
A function is a relation whose mapping is a bijection.
When is the inverse of a itself a function?
Since the inverse of a function is it's reflection over the line x=y, which has a slope of 1. The only way a function can be It'a own inverse is if it is a liner function whose slope is perpendicular to the line. Since a perpendicular line is any line with the negative recoprocal of the slope, any linear function whose slope is -1 will be it's own inverse. - stefanie math 7-12 teacher
Differentiate a relation to a function?
A function is a special type of relation. So first let's see what a relation is. A relation is a diagram, equation, or list that defines a specific relationship between groups of elements. Now a function is a relation whose every input corresponds with a single output.
What is the difference between relations and functions?
A function is a relation whose mapping is a bijection.
What do you call two opposite numbers whose sum is zero?
These are often called "opposite numbers". The more precise term is "additive inverse". For example, the additive inverse of 5 is minus 5.
What is it called if any vertical line crosses the graph of a relation more than once the relation is not a function?
The Vertical Line Test An example might be x=cos(y). At any value of x between -1 a nd +1 (a vertical line on the graph) this is multivalued (and so it is called "multivalued"). The relation is a function, because given y you can calculate x. x is a function of y. The relation between y and x can also be written y=cos-1(x) "y is the angle whose cosine is x". From that point of view you can say " y is not a function of x" because for each x, there is more than one y that satisfyies the equation. To summarize, in this example x is a function of y but y is not a function of x.
Why it is necessary for a function to be one-one for existing its inverse?
If it is not 1-1 then you will not know where the inverse value is to be mapped. For example, f(x) = x2 , being an even function, is not 1-to-1. Thus, for example, (-3)2 =9 = 32 Suppose g(x) were the inverse of f(x). What would g(9) be? -3 or 3? There is no way of telling. The only way around it is to define the domain of x to be non-negative numbers and then f would be 1-to-1 so that g was a well-defined function whose range was the non-negative numbers. Incidentally, the domain of f could just as well be defined as the non-positive numbers.
What is the inverse of 6x 8y13?
6x8y13 = 624xy whose inverse is approx 0.001603x^(-1)y^(-1)
How do you to sketch a graph of a function whose domain is in the closed interval 0-4 and whose range is the set of two numbers 2 and 3?
Find the domain of the relation then draw the graph.
What is a non example of a proportion?
A linear relationship whose graph does not pass through the origin: for example, the relation between temperatures on the Celsius and Fahrenheit scales.
Find the function whose inverse is the same as the function itself?
f ( x ) = (x-2)/(x-1)if y = (x-2)/(x-1)yx-y= x - 2yx-x= -2+yx(y-1)=y-2x = (y-2)/(y-1)so g ( x ) the inverse function is also (x-2)/(x-1)
One of two numbers whose product is one is called?
Let A and B be any two numbers such that AB=1. An example would be 1 and 1/9.We say that A is the multiplicative inverse of B. Similarly we say that B is the multiplicative inverse of A.
