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Mathematics

Functions

Easy

Question

The range of $square root of vertical line x vertical line minus x end root text is end text$

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

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

$text If end text x greater or equal than 0 text then end text square root of vertical line x vertical line minus x end root equals square root of x minus x end root equals 0 text If end text x less than 0 text then end text square root of vertical line x vertical line minus x end root equals square root of negative x minus x end root equals square root of negative 2 x end root greater than 0 therefore text Range end text equals left square bracket 0 comma straight infinity right parenthesis$

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If $f left parenthesis x right parenthesis equals fraction numerator sin 3 x over denominator sin x end fraction comma x not equal to n pi$ then the range of f(x) is

If $f left parenthesis x right parenthesis equals fraction numerator sin 3 x over denominator sin x end fraction comma x not equal to n pi$ then the range of f(x) is

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The range of $fraction numerator x squared minus 4 over denominator x minus 2 end fraction text is end text$

The range of $fraction numerator x squared minus 4 over denominator x minus 2 end fraction text is end text$

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The range of $sec squared x plus 4 cosec squared x$ is

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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 $f left parenthesis 7 right parenthesis plus 17 cos x text is end text$

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

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

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

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) =

The domain of the function f(x) =

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

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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The domain of the function f(x) = $fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text is : end text$

The domain of the function f(x) = $fraction numerator 1 over denominator square root of vertical line x vertical line minus x end root end fraction text is : end text$

MathematicsFunctions

$text If end text f colon R rightwards arrow R text and end text g colon R rightwards arrow R text are defined by end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket text and end text g left parenthesis x right parenthesis equals left square bracket x right square bracket text for end text x element of R text , end text$ where [x] is the greatest integer not exceeding x, $text then for every end text x element of R comma f left parenthesis g left parenthesis x right parenthesis right parenthesis equals$

$text If end text f colon R rightwards arrow R text and end text g colon R rightwards arrow R text are defined by end text f left parenthesis x right parenthesis equals x minus left square bracket x right square bracket text and end text g left parenthesis x right parenthesis equals left square bracket x right square bracket text for end text x element of R text , end text$ where [x] is the greatest integer not exceeding x, $text then for every end text x element of R comma f left parenthesis g left parenthesis x right parenthesis right parenthesis equals$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals left square bracket x right square bracket comma space g left parenthesis x right parenthesis equals x minus left square bracket x right square bracket$ Then which of the following functions is the zero functions

$text If end text f left parenthesis x right parenthesis equals left square bracket x right square bracket comma space g left parenthesis x right parenthesis equals x minus left square bracket x right square bracket$ Then which of the following functions is the zero functions

MathematicsFunctions

parallel

$text If end text f left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 minus x squared end root end fraction comma space g left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 plus x squared end root end fraction text then end text left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals$

$text If end text f left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 minus x squared end root end fraction comma space g left parenthesis x right parenthesis equals fraction numerator x over denominator square root of 1 plus x squared end root end fraction text then end text left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals$

MathematicsFunctions

$text For end text x element of R minus left curly bracket 0 comma 1 right curly bracket comma less or equal than t f subscript 1 left parenthesis x right parenthesis equals 1 over x comma f subscript 2 left parenthesis x right parenthesis equals 1 minus x text and end text f subscript 3 left parenthesis x right parenthesis equals fraction numerator 1 over denominator 1 minus x end fraction$ be three given functions if a function,j(x) satisfies $open parentheses f subscript 2 ring operator J ring operator f subscript 1 close parentheses left parenthesis x right parenthesis equals f subscript 3 left parenthesis x right parenthesis comma then J left parenthesis x right parenthesis$ is equal to

$text For end text x element of R minus left curly bracket 0 comma 1 right curly bracket comma less or equal than t f subscript 1 left parenthesis x right parenthesis equals 1 over x comma f subscript 2 left parenthesis x right parenthesis equals 1 minus x text and end text f subscript 3 left parenthesis x right parenthesis equals fraction numerator 1 over denominator 1 minus x end fraction$ be three given functions if a function,j(x) satisfies $open parentheses f subscript 2 ring operator J ring operator f subscript 1 close parentheses left parenthesis x right parenthesis equals f subscript 3 left parenthesis x right parenthesis comma then J left parenthesis x right parenthesis$ is equal to

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals sin squared x plus sin squared left parenthesis x plus pi divided by 3 right parenthesis plus cos x cos left parenthesis x plus pi divided by 3 right parenthesis space a n d space g left parenthesis 5 divided by 4 right parenthesis equals 1 text then end text open parentheses g o f close parentheses left parenthesis x right parenthesis equals$

$text If end text f left parenthesis x right parenthesis equals sin squared x plus sin squared left parenthesis x plus pi divided by 3 right parenthesis plus cos x cos left parenthesis x plus pi divided by 3 right parenthesis space a n d space g left parenthesis 5 divided by 4 right parenthesis equals 1 text then end text open parentheses g o f close parentheses left parenthesis x right parenthesis equals$

MathematicsFunctions

parallel

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