Question
Domain of definition of the function
, is
Hint:
Wavy curve method
The wavy curve method (also called the method of intervals) is a strategy used to solve inequalities of the form
.
The method uses the fact that
,can only change sign at its zeroes and vertical asymptotes, so we can use the roots of
and
to sketch a graph of the function over different intervals.![blank](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAFCAYAAAB8ZH1oAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAEx0lWhwAAAAxJREFUeNpjYBhGAAAAzQABhUzAtQAAADl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIi8+Llve3gAAAABJRU5ErkJggg==)
The correct answer is: ![left parenthesis negative 10 right parenthesis union left parenthesis 12 right parenthesis union left parenthesis 2 comma infinity right parenthesis](data:image/png;base64,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)
Given,
,
....... (1)
![log subscript 10 open parentheses x cubed minus x close parentheses space w i l l space b e space w e l l space d i e f i n e d space i f space x cubed space minus x space greater than 0](data:image/png;base64,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)
x(x-1)(x+1) > 0
By wavy curve method
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/1718519/1/903538/633fc4d7-3d92-4236-bfcf-0643c3aa4d61.jfif)
When x> 1, function is positive
When x lies between 0 and 1, function is negative
When x lies between -1 and 0, function is positive
When x lies between < -1 , function is negative
![T h u s comma space d o m a i n space for all x space element of left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma infinity right parenthesis space..... space left parenthesis 2 right parenthesis
T h u s comma space d o m a i n space o f space d e f i n i t i o n space left parenthesis negative 1 comma 0 right parenthesis union left parenthesis 1 comma 2 right parenthesis union left parenthesis 2 comma infinity right parenthesis](data:image/png;base64,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)
Related Questions to study
If
represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between ![w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript](data:image/png;base64,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)
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)
If
represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between ![w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript](data:image/png;base64,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)
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)
Given below is a graph between a variable force
(along
-axis) and the displacement
(along
-axis) of a particle in one dimension. The work done by the force in the displacement interval between
and
is
![](data:image/png;base64,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)
Given below is a graph between a variable force
(along
-axis) and the displacement
(along
-axis) of a particle in one dimension. The work done by the force in the displacement interval between
and
is
![](data:image/png;base64,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)
A particle of mass
moving with a velocity
makes an elastic one dimensional collision with a stationary particle of mass
establishing a contact with it for extremely small time
. Their force of contact increases from zero to
linearly in time
, remains constant for a further time
and decreases linearly from
to zero in further time
as shown. The magnitude possessed by
is
![](data:image/png;base64,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)
A particle of mass
moving with a velocity
makes an elastic one dimensional collision with a stationary particle of mass
establishing a contact with it for extremely small time
. Their force of contact increases from zero to
linearly in time
, remains constant for a further time
and decreases linearly from
to zero in further time
as shown. The magnitude possessed by
is
![](data:image/png;base64,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)
Let
be a set containing 10 distinct elements, then the total number of distinct functions from
to
is-
The domain is defined as the set which is to input in a function. We say that input values satisfy a function. The range is defined as the actual output supposed to be obtained by entering the domain of the function.
Co-domain is defined as the values that are present in the right set that is set Y, possible values expected to come out after entering domain values.
Let
be a set containing 10 distinct elements, then the total number of distinct functions from
to
is-
The domain is defined as the set which is to input in a function. We say that input values satisfy a function. The range is defined as the actual output supposed to be obtained by entering the domain of the function.
Co-domain is defined as the values that are present in the right set that is set Y, possible values expected to come out after entering domain values.