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Maths-

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Question

Consider the function $f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals x open parentheses 1 minus x to the power of 2 end exponent close parentheses$ then which of the following does not hold good?

(gof) (x) is even as well as odd
(fog)(x) is neither continuous nor differentiable for some x on $(- ¥ ̸ ¥,)$
(fog)(x) is neither odd nor even
(gof)(x) is continuous and differentiable for every ‘x’ on $(- ¥ ̸ ¥,)$

The correct answer is: (fog)(x) is neither odd nor even

$table row cell f open parentheses x close parentheses equals sgn invisible function application open parentheses x close parentheses comma g open parentheses x close parentheses equals x open parentheses 1 minus x to the power of 2 end exponent close parentheses end cell row cell open parentheses g o f close parentheses open parentheses x close parentheses equals 0 text end text text a end text text n end text text d end text text end text open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell end table$
= $table row cell 1 comma blank text end text text i end text text f end text text end text end cell row cell 0 comma blank text end text text i end text text f end text text end text end cell row cell negative 1 comma blank text end text text i end text text f end text text end text end cell end table table row cell x stack ı with hat on top open parentheses negative not equal to comma negative 1 close parentheses stack E with dot on top open parentheses 01 close parentheses end cell row cell x equals 1 open parentheses text or end text close parentheses minus 1 open parentheses text or end text close parentheses 0 end cell row cell x stack ı with hat on top open parentheses negative 10 close parentheses stack E with dot on top open parentheses 1 comma not equal to close parentheses end cell end table$

Related Questions to study

The domain of the function $square root of 1 minus f left parenthesis x right parenthesis end root text where end text f to the power of 3 end exponent left parenthesis x right parenthesis equals 1 minus x to the power of 3 end exponent minus 3 x f left parenthesis x right parenthesis. x element of R text is end text left parenthesis f left parenthesis 1 right parenthesis not equal to negative 1 right parenthesis$

The domain of the function $square root of 1 minus f left parenthesis x right parenthesis end root text where end text f to the power of 3 end exponent left parenthesis x right parenthesis equals 1 minus x to the power of 3 end exponent minus 3 x f left parenthesis x right parenthesis. x element of R text is end text left parenthesis f left parenthesis 1 right parenthesis not equal to negative 1 right parenthesis$

If $f left parenthesis x right parenthesis equals s i n to the power of negative 1 end exponent invisible function application x text and end text g left parenthesis x right parenthesis equals left square bracket s i n invisible function application x left parenthesis c o s invisible function application x right parenthesis right square bracket plus left square bracket c o s invisible function application left parenthesis s i n invisible function application x right parenthesis right square bracket comma text end text$ then range of f(g(x)) is

If $f left parenthesis x right parenthesis equals s i n to the power of negative 1 end exponent invisible function application x text and end text g left parenthesis x right parenthesis equals left square bracket s i n invisible function application x left parenthesis c o s invisible function application x right parenthesis right square bracket plus left square bracket c o s invisible function application left parenthesis s i n invisible function application x right parenthesis right square bracket comma text end text$ then range of f(g(x)) is

Domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of l n invisible function application c o t to the power of negative 1 end exponent invisible function application x end root end fraction$ is

Domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of l n invisible function application c o t to the power of negative 1 end exponent invisible function application x end root end fraction$ is

parallel

If $f colon left parenthesis 0 comma pi right parenthesis rightwards arrow R$ defined by $f open parentheses x close parentheses equals stretchy sum from k equals 1 to n of open square brackets 1 plus sin invisible function application k x close square brackets comma$ where [x] denotes the integral part of x, then range of f(x) is

If $f colon left parenthesis 0 comma pi right parenthesis rightwards arrow R$ defined by $f open parentheses x close parentheses equals stretchy sum from k equals 1 to n of open square brackets 1 plus sin invisible function application k x close square brackets comma$ where [x] denotes the integral part of x, then range of f(x) is

If [x] denotes the integral part of x, then domain of the function $f left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction plus s i n to the power of negative 1 end exponent invisible function application open square brackets fraction numerator 3 x minus 2 over denominator 2 end fraction close square brackets$ is

If [x] denotes the integral part of x, then domain of the function $f left parenthesis x right parenthesis equals fraction numerator square root of 3 minus x end root over denominator left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end fraction plus s i n to the power of negative 1 end exponent invisible function application open square brackets fraction numerator 3 x minus 2 over denominator 2 end fraction close square brackets$ is

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line t a n invisible function application x vertical line minus t a n invisible function application x end root end fraction$ is

The domain of the function $f left parenthesis x right parenthesis equals fraction numerator 1 over denominator square root of vertical line t a n invisible function application x vertical line minus t a n invisible function application x end root end fraction$ is

parallel

The domain of definition of the function $Error converting from MathML to accessible text.$

The domain of definition of the function $Error converting from MathML to accessible text.$

Let $f colon left square bracket negative 1 , 1 right square bracket rightwards arrow R$ be a function defined as $y equals f left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals l o g subscript 2 e end subscript invisible function application left square bracket x right square bracket$ ; ([.] denotes greatest integer function) then number of integers in the domain of f (g(x)) is/are

Let $f colon left square bracket negative 1 , 1 right square bracket rightwards arrow R$ be a function defined as $y equals f left parenthesis x right parenthesis text and end text g left parenthesis x right parenthesis equals l o g subscript 2 e end subscript invisible function application left square bracket x right square bracket$ ; ([.] denotes greatest integer function) then number of integers in the domain of f (g(x)) is/are

Statement - I : Let f(x) be a function such that $f left parenthesis x minus 1 right parenthesis plus f left parenthesis x plus 1 right parenthesis equals square root of 2 f left parenthesis x right parenthesis$ for all x $element of$ R then f is periodic
Statement - II : There exists a function with period 8

Statement - I : Let f(x) be a function such that $f left parenthesis x minus 1 right parenthesis plus f left parenthesis x plus 1 right parenthesis equals square root of 2 f left parenthesis x right parenthesis$ for all x $element of$ R then f is periodic
Statement - II : There exists a function with period 8

parallel

An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

An ellipse has foci at (9, 20) and (49, 55) in the xy-plane and is tangent to the x axis. The length of its major axis is :

If the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent minus 3 end fraction minus fraction numerator y to the power of 2 end exponent over denominator a plus 4 end fraction equals 1$ is inscribed in square of side length $a square root of 2 comma$ then a is

If the ellipse $fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent minus 3 end fraction minus fraction numerator y to the power of 2 end exponent over denominator a plus 4 end fraction equals 1$ is inscribed in square of side length $a square root of 2 comma$ then a is

The area of the quadrilateral formed by the tangents at the ends of latus-rectum of $5 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent equals 45$ is

The area of the quadrilateral formed by the tangents at the ends of latus-rectum of $5 x to the power of 2 end exponent plus 9 y to the power of 2 end exponent equals 45$ is

parallel

In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is $square root of 10 minus square root of 5$ The equation of the ellipse

In the standard ellipse, the lines joining the ends of the minor axis to one focus are at right angles. The distance between the focus and the nearer vertex is $square root of 10 minus square root of 5$ The equation of the ellipse

Three metal ions x⁺², y⁺², z⁺² are identify in qualitative analysis. Nitrates of x⁺², y⁺², z⁺² dissolve in three seprate test tubes and gives following observation.
i) All solution produce carbonate precipitate with (NH₄)₂CO₃
ii) Only one produce white ppt on addition of NaCl.
iii) Out of 3 cations two produce sulphide ppt.
iv) Sulphide of y⁺² is not produce by H₂S/H⁺but produce when H₂S is passed in basic medium.
v) Only y⁺² produce soluble sulphate
vi) x ⁺² gives no ppt with dil NH₄OH
Select correct about xCO₃ , y CO₃ , z CO₃ -

Three metal ions x⁺², y⁺², z⁺² are identify in qualitative analysis. Nitrates of x⁺², y⁺², z⁺² dissolve in three seprate test tubes and gives following observation.
i) All solution produce carbonate precipitate with (NH₄)₂CO₃
ii) Only one produce white ppt on addition of NaCl.
iii) Out of 3 cations two produce sulphide ppt.
iv) Sulphide of y⁺² is not produce by H₂S/H⁺but produce when H₂S is passed in basic medium.
v) Only y⁺² produce soluble sulphate
vi) x ⁺² gives no ppt with dil NH₄OH
Select correct about xCO₃ , y CO₃ , z CO₃ -

chemistry-General

Read the following comprehension carefully and answer the following questions

Read the following comprehension carefully and answer the following questions

chemistry-General

parallel

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