MCQ
If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $
- ✓$1$
- B$-1$
- C$2$
- D$4$
$ = g\,\left\{ {f\left( {\frac{{ - 5}}{3}} \right)} \right\} - f\left\{ {g\left( {\frac{{ - 5}}{3}} \right)} \right\} = g( - 2) - f\left( {\frac{5}{3}} \right) = 2 - 1 = 1$ .
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$\begin{gathered}
f\left( x \right) = \left[ \begin{gathered}
{\cos ^{ - 1}}\left( \mu \right) + {x^2},0 < x < 1 \hfill \\
4x\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x \geqslant 1 \hfill \\
\end{gathered} \right.,f\left( x \right) \hfill \\
\hfill \\ \end{gathered}$ can have a local minimum at $x =$ $1$, if the value of $\mu$ lies in the interval