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Mathematics

Functions

Easy

Question

$f colon left square bracket negative 3 comma 3 right square bracket not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x cubed plus sin x plus open square brackets fraction numerator x squared plus 2 over denominator a end fraction close square brackets space text be an odd function when end text left square bracket times right square bracket text end text$
denotes greatest integer function then a is

$< 11$
$= 11$
$> 11$
$none$

The correct answer is: $greater than 11$

$f left parenthesis negative x right parenthesis equals negative f left parenthesis x right parenthesis not stretchy rightwards double arrow open square brackets fraction numerator x squared plus 2 over denominator a end fraction close square brackets equals 0 not stretchy rightwards double arrow 0 less or equal than fraction numerator x squared plus 2 over denominator a end fraction less than 1 x element of left square bracket negative 3 comma 3 right square bracket not stretchy rightwards double arrow x squared plus 2 less than 11 therefore a greater than 11$

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Among the following functions defined on R into R, the constant function is

Among the following functions defined on R into R, the constant function is

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$text Let end text f left parenthesis x right parenthesis equals fraction numerator x over denominator e to the power of x minus 1 end fraction plus x over 2 plus 1 comma text then end text f text is end text$

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$text If end text f left parenthesis x right parenthesis equals fraction numerator a to the power of x minus 1 over denominator x to the power of n open parentheses a to the power of x plus 1 close parentheses end fraction$ is even then n =

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