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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.
What is the inverse tangent of 1.4737?
The inverse tangent, denoted as arctan or tan^(-1), of 1.4737 is approximately 56.05 degrees when measured in degrees or approximately 0.980 radians when measured in radians. This value represents the angle whose tangent is 1.4737. In trigonometry, the inverse tangent function helps determine the angle when the tangent ratio is known.
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.
What is the inverse of 6x 8y13?
6x8y13 = 624xy whose inverse is approx 0.001603x^(-1)y^(-1)
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.
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.
What is the inverse tangent of 1.4737?
The inverse tangent, denoted as arctan or tan^(-1), of 1.4737 is approximately 56.05 degrees when measured in degrees or approximately 0.980 radians when measured in radians. This value represents the angle whose tangent is 1.4737. In trigonometry, the inverse tangent function helps determine the angle when the tangent ratio is known.
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)
