Let g(x) = 1 + x - [x] and f(x)= -1,&x 0 where [x] denotes the greatest integer less than or equal to x. Then for all x, f(g(x)) is equal to:

Let g(x) = 1 + x - [x] and f(x)= -1,&x<0 0,&x=0 1,&x>0 where [x] …

Choose the correct option from given four options:
$\int\frac{\text{x}}{\text{x}+1}$ is equal to:

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$\int_{}^{} {{{\tan }^{ - 1}}x\,dx = } $

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What are the direction cosines of a line which is equally inclined to the positive directions of the axes:

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The area enclosed between the curve $\text{y}=\log_{\text{e}}(\text{x}+\text{e}),\text{x}=\log_\text{e}\Big(\frac{1}{\text{y}}\Big)$ and the $x-$axis is:

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Area bounded by parabola $y^2 = x$ and straight line $2y = x$ is:

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If the maximum value of $a$, for which the function $f_{a}(x)=\tan ^{-1} 2 x-3 a x+7$ is non-decreasing in $\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$, is $\bar{a}$, then $f_{a}\left(\frac{\pi}{8}\right)$ is equal to

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If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by 'x is greater than y'. The range of R is:

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In $( - 4,\,4)$ the function $f(x) = \int\limits_{ - 10}^x {({t^4} - 4){e^{ - 4t}}dt} $ has

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If $\text{f(x)}=\text{a}|\sin\text{x}|+\text{be}^{|\text{x}|}+\text{c|x|}^3$and if $f(x)$ is differentiable at $x = 0,$ then :

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The number that exceeds its square by the greatest amount is

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