Maths-
General
Easy
Question
If f
= x + 2 then
is equal to
- None of these
The correct answer is: ![negative 8 over 3 l n invisible function application space straight l space left parenthesis 1 minus x right parenthesis ∣ plus 2 over 3 x plus c](data:image/png;base64,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)
Related Questions to study
maths-
Let
, then
is equal to:
Let
, then
is equal to:
maths-General
maths-
Statement I : y = f(x) =
, x
R Range of f(x) is [3/4, 1)
Statement II :
.
Statement I : y = f(x) =
, x
R Range of f(x) is [3/4, 1)
Statement II :
.
maths-General
maths-
Statement I : Function f(x) = sinx + {x} is periodic with period ![2 pi](data:image/png;base64,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)
Statement II : sin x and {x} are both periodic with period
and 1 respectively.
Statement I : Function f(x) = sinx + {x} is periodic with period ![2 pi](data:image/png;base64,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)
Statement II : sin x and {x} are both periodic with period
and 1 respectively.
maths-General
maths-
Statement 1 : f : R
R and
is bijective.
Statement 2 :
is bijective.
Statement 1 : f : R
R and
is bijective.
Statement 2 :
is bijective.
maths-General
maths-
Statement I : Graph of y = tan x is symmetrical about origin
Statement II : Graph of
is symmetrical about y-axis
Statement I : Graph of y = tan x is symmetrical about origin
Statement II : Graph of
is symmetrical about y-axis
maths-General
maths-
Statement-
If
Where
is an identity function.
Statement-
R defined by
is an identity function.
Statement-
If
Where
is an identity function.
Statement-
R defined by
is an identity function.
maths-General
Maths-
Assertion (A) :
Graph of ![open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text and end text x comma y element of R close curly brackets](data:image/png;base64,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)
Reason (R) : In the expression am/n, where a, m, n × J+, m represents the power to which a is be raised, whereas n determines the root to be taken; these two processes may be administered in either order with the same result.
Assertion (A) :
Graph of ![open curly brackets left parenthesis x comma y right parenthesis divided by y equals 2 to the power of negative x end exponent text and end text x comma y element of R close curly brackets](data:image/png;base64,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)
Reason (R) : In the expression am/n, where a, m, n × J+, m represents the power to which a is be raised, whereas n determines the root to be taken; these two processes may be administered in either order with the same result.
Maths-General
maths-
Assertion: The period of
is 1/2.
Reason: The period of x – [x] is 1.
Assertion: The period of
is 1/2.
Reason: The period of x – [x] is 1.
maths-General
Maths-
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Maths-General
Maths-
Assertion: The function defined by
is invertible if and only if
.
Reason: A function is invertible if and only if it is one-to-one and onto function.
Assertion: The function defined by
is invertible if and only if
.
Reason: A function is invertible if and only if it is one-to-one and onto function.
Maths-General
Maths-
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Assertion :
can never become positive.
Reason : f(x) = sgn x is always a positive function.
Maths-General
Maths-
If f (x) = ![open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f left parenthesis x right parenthesis d x equals close](data:image/png;base64,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)
If f (x) = ![open curly brackets table row cell e to the power of cos invisible function application x end exponent end cell cell sin invisible function application x text for end text vertical line x vertical line less or equal than 2 end cell row cell text 2, end text end cell cell text otherwise end text end cell end table comma text then end text not stretchy integral subscript text -2 end text end subscript superscript 3 end superscript f left parenthesis x right parenthesis d x equals close](data:image/png;base64,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)
Maths-General
Maths-
The value of the integral
dx is :
The value of the integral
dx is :
Maths-General
Maths-
Assertion : Let
be a function defined by f(x) =
. Then f is many-one function.
Reason : If either
or
domain of f, then y = f(x) is one-one function.</span
Assertion : Let
be a function defined by f(x) =
. Then f is many-one function.
Reason : If either
or
domain of f, then y = f(x) is one-one function.</span
Maths-General
Maths-
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Assertion : Fundamental period of
.
Reason : If the period of f(x) is
and the period of g(x) is
, then the fundamental period of f(x) + g(x) is the L.C.M. of
and T
Maths-General