(B) Given,$f(x) = x - [x]$ and $g(x) = [x]$ for $x \in R$. We need to find the value of $f(g(x))$. By substituting $g(x)$ into $f(x)$,we get: $f(g(x))

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(B) Given,$f(x) = x - [x]$ and $g(x) = [x]$ for $x \in R$. We need to find the value of $f(g(x))$. By substituting $g(x)$ into $f(x)$,we get: $f(g(x)) = f([x])$. Since $f(x) = x - [x]$,substituting $[x]$ for $x$ gives: $f([x]) = [x] - [[x]]$. Since $[x]$ is an integer,the greatest integer function of an integer is the integer itself,i.e.,$[[x]] = [x]$. Therefore,$f([x]) = [x] - [x] = 0$. Thus,for every $x \in R, f(g(x)) = 0$.

Class 11 Chemistry Data Entry - Chemistry Level 0 of all question bank

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to

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The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

AP EAMCET 2007

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From a point on the level ground,the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole,the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

TS EAMCET 2002

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For a reaction $\frac{1}{2} A \rightarrow 2B,$ the rate of disappearance of $A$ is related to the rate of appearance of $B$ by the expression:

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The bleaching action of $SO_2$ is due to its:

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$A$ screen is placed $50\,cm$ from a single slit,which is illuminated with $6000 \mathring{A}$ light. If the distance between the first and third minima in the diffraction pattern is $3\,mm$,the width of the slit is.....$mm$.

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If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=x-[x]$ and $g(x)=[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then for every $x \in R, f(g(x))$ is equal to

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The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

From a point on the level ground,the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole,the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

For a reaction $\frac{1}{2} A \rightarrow 2B,$ the rate of disappearance of $A$ is related to the rate of appearance of $B$ by the expression:

The bleaching action of $SO_2$ is due to its:

$A$ screen is placed $50\,cm$ from a single slit,which is illuminated with $6000 \mathring{A}$ light. If the distance between the first and third minima in the diffraction pattern is $3\,mm$,the width of the slit is.....$mm$.

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