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The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

$R - {- 1,2}$
$(- 2, \infty)$
$R - {- 1, - 2, - 3}$
$(- 3, \infty) - {- 1, - 2}$

hint Hint:

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The correct answer is: $left parenthesis negative 3 comma infinity right parenthesis minus left curly bracket negative 1 comma negative 2 right curly bracket$

$f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$
For f(x) to be defined :
1) (x + 3) > 0
$rightwards double arrow$ x > -3
2) $x to the power of 2 space end exponent plus space 3 x space plus space 2 space space not equal to space 0$
$B y space f a c t o r i z a t i o n space left parenthesis s p l i t t i n g space o f space m i d d l e space t e r m s right parenthesis rightwards double arrow left parenthesis x space plus 1 right parenthesis left parenthesis x plus 2 right parenthesis space space not equal to space 0 rightwards double arrow x space space not equal to space left parenthesis negative 1 comma negative 2 right parenthesis$
Thus, Domain of f(x) will be (-3, $infinity$ ) - (-1,-2)

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

Maths-General

We used rules of indices to solve the question. For such questions, we should be familiar with rules of indices.

General

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The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

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A Shell of mass M and radius R has a point mass placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

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The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

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The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

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chemistry-

Which of the following structures have same configuration around the chirality centre ?

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The two structures given below are :

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Which of the following represents same enantiomer as :

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Calculate the d- and $l$ -isomers formed by the following compound.
$H O O C minus C H open parentheses C H subscript 3 end subscript close parentheses minus C H O H minus C H B r minus C H O H minus C H open parentheses C H subscript 3 end subscript close parentheses minus C O O H minus$

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Which of the following graphs represents the motion of a planet moving about the sun.

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The domain of is

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The correct answer is:

For f(x) to be defined :1) (x + 3) > 0x > -32) Thus, Domain of f(x) will be (-3, ) - (-1,-2)

Related Questions to study

The inverse of the function is

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A Shell of mass M and radius R has a point mass placed at a distance r from its center. The gravitational potential energy u(r)-v will be,

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The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

The correct graph representing the variation of total energy (E) kinetic energy and potential energy (U) of a satellite with its distance from the center of earth is.........

The curves for P.E. (U) K.E. (EEK) of two particle system ae shown in figure, At what points. system will be bound.

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The absolute configuration of the following compound is :

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Among the following structures which one is called Erythro isomer ?

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The domain of $f left parenthesis x right parenthesis equals fraction numerator l o g subscript 2 end subscript invisible function application left parenthesis x plus 3 right parenthesis over denominator x to the power of 2 end exponent plus 3 x plus 2 end fraction$ is

The correct answer is: $left parenthesis negative 3 comma infinity right parenthesis minus left curly bracket negative 1 comma negative 2 right curly bracket$

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

The inverse of the function $y equals open square brackets 1 minus left parenthesis x minus 3 right parenthesis to the power of 4 end exponent close square brackets to the power of 1 divided by 7 end exponent$ is

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

The domain of $f left parenthesis x right parenthesis equals square root of x to the power of 2 end exponent minus 4 vertical line x vertical line plus 3 end root$ is

Calculate the d- and $l$ -isomers formed by the following compound.
$H O O C minus C H open parentheses C H subscript 3 end subscript close parentheses minus C H O H minus C H B r minus C H O H minus C H open parentheses C H subscript 3 end subscript close parentheses minus C O O H minus$

Calculate the d- and $l$ -isomers formed by the following compound.
$H O O C minus C H open parentheses C H subscript 3 end subscript close parentheses minus C H O H minus C H B r minus C H O H minus C H open parentheses C H subscript 3 end subscript close parentheses minus C O O H minus$