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A function cannot be one to many.
Suppose y = tan(x)
Now, since tan(x) = tan(x + pi)
then tan(x + pi) = y
But that means arctan(y) can be x or x+pi
In order to prevent that sort of indeterminacy, the arctan function must be restricted to an interval of width pi.
Any interval of that width would do and it could have been restricted to the first and second quadrants, or even from -pi/4 to 3*pi/4. The problem there is that in the middle of that interval the tan function becomes infinite which means that arctan would have a discontinuity in the middle of its domain. A better option, then, is to restrict it to the first and fourth quarters. Then the asymptotic values occur at the ends of the domain, which leaves the function continuous within the whole of the open interval.
What else can I help you with?
Which circles lie completely within the fourth quadrant?
Circles that lie completely within the fourth quadrant of the Cartesian plane have their centers in the fourth quadrant and have a radius smaller than the distance from the center to the x-axis and y-axis. In other words, the circle's center coordinates (x, y) must both be positive, and the radius r must be less than both x and y. This ensures that the entire circle falls within the boundaries of the fourth quadrant.
What quadrants would a zero abscissa and a negative ordinate be in?
A point with a zero abscissa (x-coordinate) and a negative ordinate (y-coordinate) would lie in the fourth quadrant of the Cartesian coordinate system. In this quadrant, the x-coordinate is positive or zero, while the y-coordinate is negative. This means that the point would be to the right of the y-axis (positive x-direction) and below the x-axis (negative y-direction).
Find the average value of the function on the given interval fx equals 2x to the power of3 open parentheses 1 plus x squared closed to the fourth power?
You need to clarify the function AND provide an interval.
What is the word for three quarters of a circle?
The word for three quarters of a circle is "quadrant." A quadrant is a sector equal to one fourth of a circle, so three quadrants make up three quarters of a circle. Each quadrant measures 90 degrees, totaling 270 degrees for three quarters of a circle.
What is the antonym of fourth?
fourth
What are the names of the quadrants on a graph?
The names of the quadrants on a graph are: First quadrant Second quadrant Third quadrant Fourth quadrant
Is it possible for a line to pass through exactly two quadrants?
Yes, it is possible for a line to pass through exactly two quadrants. For instance, a line that has a positive slope can pass through the first and third quadrants if it extends from the second quadrant to the fourth. Similarly, a line with a negative slope can pass through the second and fourth quadrants. In both cases, the line does not intersect the axes in such a way that it enters all four quadrants.
Is it possible for a fourth degree function to have an inverse that is a function?
In order for a fourth degree function to have an inverse function, its domain must be restricted. Otherwise the inverse function will not pass the vertical-line test.Ex.f(x) = x^4 (x>0), the original functionf-1(x) = x ^ (1/4), the inverse
What can you sa about the coordinates of all points that lie on the line bisecting the second and the fourth quadrants?
They satisfy the equation x + y = 0
How many quadrants in the cartesian plane?
The Cartesian plane is divided into four quadrants. These quadrants are determined by the signs of the x and y coordinates: the first quadrant (positive x, positive y), the second quadrant (negative x, positive y), the third quadrant (negative x, negative y), and the fourth quadrant (positive x, negative y).
Function of fourth ventricle?
gay
Do x and y coordinates have opposite signs!?
Yes, x and y coordinates can have opposite signs. This occurs in the second and fourth quadrants of the Cartesian coordinate system. In the second quadrant, x is negative and y is positive, while in the fourth quadrant, x is positive and y is negative.
What is a quartic?
A quartic is an algebraic equation or function of the fourth degree.
What is the function rule of 5 less than one fourth of x is y?
That's the function rule.
What are the coordinates of a point that could be in each of the four quadrants?
The coordinates must be as follows: First quadrant: positive, positive Second quadrant: negative, positive Third quadrant: negative, negative Fourth quadrant: positive, negative
In which quardant are the terminal arms of the angle lie when sin thita is less then zero and cos thita is greater then zero?
The fourth Across the quadrants sin theta and cos theta vary: sin theta: + + - - cos theta: + - - + So for sin theta < 0, it's the third or fourth quadrant And for cos theta > 0 , it's the first or fourth quadrant. So for sin theta < 0 and cos theta > 0 it's the fourth quadrant
What are the quadrants in math?
There are four quadrants. They are represented by Roman numerals : I(one), II(two), III(three), IV(four). The first quadrant contains all positive points , (+x, +y) The second quadrant contains negative x's and positive y's , (-x, +y) The third quadrant is all negative , (-x, -y) The fourth quadrant has negative y's and positive x's , (+x, -y)
