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Mathematics

Functions

Easy

Question

$text If end text f colon R not stretchy rightwards arrow A text defined by end text f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction straight for all x element of R text is surjective, then end text A equals$

$[1, \infty)$
$(1, \infty)$
$[0, 1]$
$(0, 1]$

The correct answer is: $left parenthesis 0 comma 1 right square bracket$

$text Clearly end text f left parenthesis x right parenthesis greater than 0 space of 1em straight for all x element of R x squared plus 2 x plus 2 equals left parenthesis x plus 1 right parenthesis squared plus 1 greater or equal than 1 not stretchy rightwards double arrow fraction numerator 1 over denominator x squared plus 2 x plus 2 end fraction less or equal than 1 not stretchy rightwards double arrow f left parenthesis x right parenthesis less or equal than 1 not stretchy rightwards double arrow 0 less than f left parenthesis x right parenthesis less or equal than 1$

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If x and {x} represents integral and fractional parts of x,then $left square bracket x right square bracket plus sum from r equals 1 to 2000 of fraction numerator left curly bracket x plus r right curly bracket over denominator 2000 end fraction equals$

If x and {x} represents integral and fractional parts of x,then $left square bracket x right square bracket plus sum from r equals 1 to 2000 of fraction numerator left curly bracket x plus r right curly bracket over denominator 2000 end fraction equals$

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$text If end text f left parenthesis x right parenthesis equals a x to the power of 7 plus b x cubed plus c x minus 5 text and end text f left parenthesis negative 7 right parenthesis equals 7$ , then the range of $f left parenthesis 7 right parenthesis plus 17 cos x text is end text$

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Domain of $text end text f left parenthesis x right parenthesis equals sin to the power of negative 1 end exponent x plus Sec to the power of negative 1 end exponent x text is end text$

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The domain of the function $f left parenthesis x right parenthesis equals log subscript 3 plus x end subscript open parentheses x squared minus 1 close parentheses text is end text$

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The domain of $text end text f left parenthesis x right parenthesis equals open parentheses fraction numerator 1 over denominator vertical line x vertical line minus 1 end fraction close parentheses to the power of 1 over 2006 end exponent text is end text$

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The domain of the function f(x) =

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The domain of $square root of left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis left parenthesis x minus 3 right parenthesis end root text is end text$

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