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Mathematics

Functions

Easy

Question

$text If end text straight f left parenthesis straight x right parenthesis text is a function such that end text f left parenthesis x y right parenthesis equals f left parenthesis x right parenthesis plus f left parenthesis y right parenthesis text and end text f left parenthesis 2 right parenthesis equals 1 text then end text straight f left parenthesis straight x right parenthesis equals$

$x^{2}$
$2^{x}$
$\log_{2} x$
$\log_{x} 2$

The correct answer is: $log subscript 2 x$

$f left parenthesis x y right parenthesis equals f left parenthesis x right parenthesis plus f left parenthesis y right parenthesis not stretchy rightwards double arrow f left parenthesis x right parenthesis equals log subscript a x f left parenthesis 2 right parenthesis equals 1 not stretchy rightwards double arrow log subscript a 2 equals 1 not stretchy rightwards double arrow a equals 2 therefore f left parenthesis x right parenthesis equals log subscript 2 x$

Related Questions to study

$text If end text straight f left parenthesis straight x right parenthesis text is a function such that end text f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis text and end text f left parenthesis 3 right parenthesis equals 125 text then end text straight f left parenthesis straight x right parenthesis equals$

$text If end text straight f left parenthesis straight x right parenthesis text is a function such that end text f left parenthesis x plus y right parenthesis equals f left parenthesis x right parenthesis f left parenthesis y right parenthesis text and end text f left parenthesis 3 right parenthesis equals 125 text then end text straight f left parenthesis straight x right parenthesis equals$

MathematicsFunctions

If f(x) is a polynomial function such that $f left parenthesis x right parenthesis f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text and end text f left parenthesis 3 right parenthesis equals negative 80$ then f(x)

If f(x) is a polynomial function such that $f left parenthesis x right parenthesis f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text and end text f left parenthesis 3 right parenthesis equals negative 80$ then f(x)

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis text is a polynomial function satisfying end text f left parenthesis x right parenthesis times f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text and end text f left parenthesis 4 right parenthesis equals 257 comma text then end text f left parenthesis 3 right parenthesis equals$

$text If end text f left parenthesis x right parenthesis text is a polynomial function satisfying end text f left parenthesis x right parenthesis times f open parentheses 1 over x close parentheses equals f left parenthesis x right parenthesis plus f open parentheses 1 over x close parentheses text and end text f left parenthesis 4 right parenthesis equals 257 comma text then end text f left parenthesis 3 right parenthesis equals$

MathematicsFunctions

parallel

The set of all values of a for which the function $f colon R rightwards arrow R text given by end text$
$f left parenthesis x right parenthesis equals x cubed plus left parenthesis a plus 2 right parenthesis x squared plus 3 a x plus 5 text is one-one is end text$

The set of all values of a for which the function $f colon R rightwards arrow R text given by end text$
$f left parenthesis x right parenthesis equals x cubed plus left parenthesis a plus 2 right parenthesis x squared plus 3 a x plus 5 text is one-one is end text$

MathematicsFunctions

Let f: (-1,1) → B, be a function defined by $f left parenthesis x right parenthesis equals t an to the power of negative 1 end exponent fraction numerator 2 x over denominator 1 minus x squared end fraction$ then f is both one-one and onto when B is the interval

Let f: (-1,1) → B, be a function defined by $f left parenthesis x right parenthesis equals t an to the power of negative 1 end exponent fraction numerator 2 x over denominator 1 minus x squared end fraction$ then f is both one-one and onto when B is the interval

MathematicsFunctions

$text The function end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 0 comma straight infinity right parenthesis text defined by end text f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus x end fraction text is end text$

$text The function end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow left square bracket 0 comma straight infinity right parenthesis text defined by end text f left parenthesis x right parenthesis equals fraction numerator x over denominator 1 plus x end fraction text is end text$

MathematicsFunctions

parallel

Let A = { x ε R : x is not a positive integer }. Define a function f : A → R as $f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x minus 1 end fraction text then end text f text is end text$

Let A = { x ε R : x is not a positive integer }. Define a function f : A → R as $f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x minus 1 end fraction text then end text f text is end text$

MathematicsFunctions

$text If end text f colon N not stretchy rightwards arrow bold italic R text is defined by end text f left parenthesis 1 right parenthesis equals negative 1 text and end text f left parenthesis n plus 1 right parenthesis equals 3 f left parenthesis n right parenthesis plus 2 text for end text n greater than 1 comma text then end text f text is end text$

$text If end text f colon N not stretchy rightwards arrow bold italic R text is defined by end text f left parenthesis 1 right parenthesis equals negative 1 text and end text f left parenthesis n plus 1 right parenthesis equals 3 f left parenthesis n right parenthesis plus 2 text for end text n greater than 1 comma text then end text f text is end text$

MathematicsFunctions

$text Define end text f colon Z not stretchy rightwards arrow Z text by end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell x divided by 2 end cell cell left parenthesis x text is even end text right parenthesis end cell row 0 cell left parenthesis x text is odd end text right parenthesis end cell end table close text then end text f text is end text$

$text Define end text f colon Z not stretchy rightwards arrow Z text by end text f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell x divided by 2 end cell cell left parenthesis x text is even end text right parenthesis end cell row 0 cell left parenthesis x text is odd end text right parenthesis end cell end table close text then end text f text is end text$

MathematicsFunctions

parallel

$text If end text f colon R not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x comma text if end text x greater than 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 5 x minus 2 comma text if end text x less or equal than 2 comma space space text then end text f text is end text space$

$text If end text f colon R not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x comma text if end text x greater than 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 5 x minus 2 comma text if end text x less or equal than 2 comma space space text then end text f text is end text space$

MathematicsFunctions

For real x, $text let end text f left parenthesis x right parenthesis equals x cubed plus 5 x plus 1 comma text end text$ then

For real x, $text let end text f left parenthesis x right parenthesis equals x cubed plus 5 x plus 1 comma text end text$ then

MathematicsFunctions

$text If end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x squared comma text then end text f text is end text$

$text If end text f colon left square bracket 0 comma straight infinity right parenthesis not stretchy rightwards arrow R text defined by end text f left parenthesis x right parenthesis equals x squared comma text then end text f text is end text$

MathematicsFunctions

parallel

$text If end text f colon R not stretchy rightwards arrow R text is defined by end text f left parenthesis x right parenthesis equals 2 x plus vertical line x vertical line text then end text f left parenthesis 2 x right parenthesis plus f left parenthesis negative x right parenthesis minus f left parenthesis x right parenthesis equals$

$text If end text f colon R not stretchy rightwards arrow R text is defined by end text f left parenthesis x right parenthesis equals 2 x plus vertical line x vertical line text then end text f left parenthesis 2 x right parenthesis plus f left parenthesis negative x right parenthesis minus f left parenthesis x right parenthesis equals$

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos squared x plus sin to the power of 4 x over denominator sin squared x plus cos to the power of 4 x end fraction text for x∈R end text$ then f(2002) =

$text If end text f left parenthesis x right parenthesis equals fraction numerator cos squared x plus sin to the power of 4 x over denominator sin squared x plus cos to the power of 4 x end fraction text for x∈R end text$ then f(2002) =

MathematicsFunctions

$text If end text f left parenthesis x right parenthesis equals 4 x minus 1 comma text if end text x greater than 4 comma space space space space space space space space space space space equals x squared minus 2 comma text if end text minus 2 less or equal than x less or equal than 3 comma space space space space space space space space space space space space equals 3 x plus 4 comma text if end text x less than negative 2 comma t h e n space fraction numerator f left parenthesis negative 3 right parenthesis plus f left parenthesis 5 right parenthesis plus f left parenthesis 0 right parenthesis plus f left parenthesis negative 1 right parenthesis over denominator f left parenthesis negative 2 right parenthesis plus f left parenthesis 1 right parenthesis plus f left parenthesis negative 5 right parenthesis plus f left parenthesis 3 right parenthesis end fraction equals$

$text If end text f left parenthesis x right parenthesis equals 4 x minus 1 comma text if end text x greater than 4 comma space space space space space space space space space space space equals x squared minus 2 comma text if end text minus 2 less or equal than x less or equal than 3 comma space space space space space space space space space space space space equals 3 x plus 4 comma text if end text x less than negative 2 comma t h e n space fraction numerator f left parenthesis negative 3 right parenthesis plus f left parenthesis 5 right parenthesis plus f left parenthesis 0 right parenthesis plus f left parenthesis negative 1 right parenthesis over denominator f left parenthesis negative 2 right parenthesis plus f left parenthesis 1 right parenthesis plus f left parenthesis negative 5 right parenthesis plus f left parenthesis 3 right parenthesis end fraction equals$

MathematicsFunctions

parallel

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