A) {0, 1}
B) {1, 2}
C) {-3, -2}
D) {2, 3}
Correct Answer: C
Solution :
Given, \[\operatorname{f}(x)=\,\,\left| x \right|\,\,and g(x)=\,\,\left[ x\,-3 \right]\] For \[-\frac{8}{5}<x<\frac{8}{5};\,\,\,0\le \,\,f\,(x)<\frac{8}{5}\] Now, for \[0\le f(x)<1,\] \[g(f(x))=[f(x)-3]=-\,3[\because \,\,\,-3\le f(x)-3<-\,2]\] \[\operatorname{for}\,\,1\le f(x)<1.6\] \[\operatorname{g}(f(x))=-\,2\,\,\,\,\,\,\,\,\,\,[\because \,\,-2\,\le \,\,f(x)-\,3\,<\,-1.4]\] \[\therefore \,\, required set is \left\{ -3,\,\,-2 \right\}.\]You need to login to perform this action.
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