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Maths-

General

Easy

Question

Let $f left parenthesis x right parenthesis equals a x plus b$ where c is a variable coefficient and $x greater than fraction numerator 7 over denominator 6 end fraction$ The value of c such that f(x) touches $f to the power of negative 1 end exponent$ (x), is

6
7
$\frac{16}{3}$
$\frac{4}{3}$

The correct answer is: $fraction numerator 16 over denominator 3 end fraction$

f(x) and $f to the power of negative 1 end exponent left parenthesis x right parenthesis$ can only intersect on the line y=x and therefore y=x must be tangent at the comman point of tangency
$3 x to the power of 2 end exponent minus 7 x plus c minus x$
$3 x to the power of 2 end exponent minus 8 x plus c equals 0. horizontal ellipsis left parenthesis 1 right parenthesis$
Put $D equals 0$
$64 minus 12 c equals 0 rightwards double arrow c equals fraction numerator 64 over denominator 12 end fraction equals fraction numerator 16 over denominator 3 end fraction$
$1 equals 6 x minus 7 rightwards double arrow x equals fraction numerator 4 over denominator 3 end fraction$
From ((a) put $x equals 4 divided by 3 text to get end text c equals fraction numerator 16 over denominator 3 end fraction$

Related Questions to study

The domain of function, satisfying $f left parenthesis x right parenthesis plus f open parentheses x to the power of negative 1 end exponent close parentheses equals fraction numerator x to the power of 3 end exponent plus 1 over denominator x end fraction$

The domain of function, satisfying $f left parenthesis x right parenthesis plus f open parentheses x to the power of negative 1 end exponent close parentheses equals fraction numerator x to the power of 3 end exponent plus 1 over denominator x end fraction$

The range of the function $f left parenthesis x right parenthesis equals square root of x minus 1 end root plus 2 square root of 3 minus x end root$ is

The range of the function $f left parenthesis x right parenthesis equals square root of x minus 1 end root plus 2 square root of 3 minus x end root$ is

$f colon R rightwards arrow R$ Statement 1 : $f left parenthesis x right parenthesis equals 12 x to the power of 5 end exponent minus 15 x to the power of 4 end exponent plus 20 x to the power of 3 end exponent minus 30 x to the power of 2 end exponent plus 60 x plus 1$ is monotonic and surjective on R because, Statement 2 : A continuous function defined on R, if strictly monotonic has its range R

$f colon R rightwards arrow R$ Statement 1 : $f left parenthesis x right parenthesis equals 12 x to the power of 5 end exponent minus 15 x to the power of 4 end exponent plus 20 x to the power of 3 end exponent minus 30 x to the power of 2 end exponent plus 60 x plus 1$ is monotonic and surjective on R because, Statement 2 : A continuous function defined on R, if strictly monotonic has its range R

parallel

Graph of $y equals vertical line 4 x minus 5 vertical line minus$ is

Graph of $y equals vertical line 4 x minus 5 vertical line minus$ is

If $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are non periodic function then $h left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis$ is

If $f left parenthesis x right parenthesis$ and $g left parenthesis x right parenthesis$ are non periodic function then $h left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis$ is

If $a less or equal than fraction numerator s e c to the power of 2 end exponent invisible function application theta minus t a n invisible function application theta over denominator s e c to the power of 2 end exponent invisible function application theta plus t a n invisible function application theta end fraction less or equal than b$ then a+b=

If $a less or equal than fraction numerator s e c to the power of 2 end exponent invisible function application theta minus t a n invisible function application theta over denominator s e c to the power of 2 end exponent invisible function application theta plus t a n invisible function application theta end fraction less or equal than b$ then a+b=

parallel

The set of values of a for which the equation $blank x to the power of 3 end exponent minus 3 x plus a equals 0$ has three distinct real roots is

The set of values of a for which the equation $blank x to the power of 3 end exponent minus 3 x plus a equals 0$ has three distinct real roots is

Let $text end text alpha text end text$ and $text end text beta text end text$ be the roots of the equation $text end text x to the power of 2 end exponent minus p x plus r equals 0 text end text$ and $text end text fraction numerator alpha over denominator 2 end fraction text , end text blank 2 beta text end text$ be the roots of the equation $x to the power of 2 end exponent minus q x plus r equals 0 text . end text$ The value of $text end text text end text r text end text$ is

Let $text end text alpha text end text$ and $text end text beta text end text$ be the roots of the equation $text end text x to the power of 2 end exponent minus p x plus r equals 0 text end text$ and $text end text fraction numerator alpha over denominator 2 end fraction text , end text blank 2 beta text end text$ be the roots of the equation $x to the power of 2 end exponent minus q x plus r equals 0 text . end text$ The value of $text end text text end text r text end text$ is

The molecules and are

The molecules and are

Chemistry-General

parallel

The correct IUPAC name of

The correct IUPAC name of

Chemistry-General

In which of the compound given below contains more than one kind of hybridization (sp² , sp³ ) for carbon

In which of the compound given below contains more than one kind of hybridization (sp² , sp³ ) for carbon

Chemistry-General

Oxygen as a super oxide is in the form of

Oxygen as a super oxide is in the form of

Chemistry-General

parallel

Toluene has

Toluene has

Chemistry-General

Which of the following statement is not correct?

Which of the following statement is not correct?

Chemistry-General

Which of the following pairs contains mixed oxides ?

Which of the following pairs contains mixed oxides ?

Chemistry-General

parallel

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