Find fog and gof if:f(x)=c,c R,g(x)= x^2 - Vidyadip

Question

Find fog and gof if:$\text{f}(\text{x})=\text{c},\text{c}\in \text{R},\text{g(x)}=\sin \text{x}^2$

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Answer

$\text{f} \ \text{x}=\text{c} = \sin \text{x} \ 2\ \text{f}:\text{R}\ \rightarrow{\ } \ \text{c};\text{g}:\text{R}\ \rightarrow{\ } \ 0,1$
Computing fog: Clearly, the range of g is a subset of the domain of f.
$.\text{fog}:\text{R}\ \rightarrow{\ }\ \text{x}=\text{f}\ \text{g}\text{ x }=\text{f} \ \sin \text{x}^2=\text{c}$
Computing gof: Clearly, the range of f is a subset of the domain of g.
$\Rightarrow \text{fog}: \text{R}\ \rightarrow{\ }\text{x}=\text{g}\ \text{f}\ \text{x}=\text{g}\ \text{c}=\sin \text{c}^2$

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