A cart of mass $0.5kg$ is placed on a smooth surface and is connected by a string to a block of mass $0.2kg.$ At the initial moment the cart moves to the left along a horizontal plane at a speed of \displaystyle{7}{m}/{s}{\left(\text{Use }\ {g}={9.8}{m}/{s}^{{{2}}}\right)}

The domain of the function $f(x)={\sin }^{-1}[{\log }_g(x/2)]$ is

The domain of the function $f(x)=\frac{1}{\sqrt{\left\{\sin x\right\}+\left\{\sin (\pi +x)\right\}}}$, where {.} denotes the fractional part, is

Write the domain of $f(x)={\cos }^{-1}x$.

The domain of definition of function $f(x)=\frac{1+2(x+4{)}^{-0.5}}{2-(x+4{)}^{0.5}}+(x+4{)}^{0.5}+4(x+4{)}^{0.5}$ is

If [.] denotes the greatest integer function then the domain of the real valued function ${\log }_{[x+1/2]}\left|x^2-x-2\right|$ is

Find the domain of $x$ if  $f(x)=\sqrt{x^2-|x|-2}$

The domain of the function $\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{|\mathrm{x}|-\mathrm{x}}}$ is

Find the Domain of function$f(t)=\frac{1}{t^2+2t-t-2}$

The domain of the function $f(x)=\frac{1}{\sqrt{4-x^2}}$ is