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Question Number 31611 by mondodotto@gmail.com last updated on 11/Mar/18

Commented by mondodotto@gmail.com last updated on 11/Mar/18

$$\mathrm{please}\mathrm{help}$$

Answered by Rasheed.Sindhi last updated on 11/Mar/18

$$g\mathrm{o}f\left(x\right)=g\left(f\left(x\right)\right):x\in \{1,2,3,4\}$$$$g\mathrm{o}f\left(1\right)=g\left(f\left(1\right)\right)=g\left(4\right)=4$$$$g\mathrm{o}f\left(2\right)=g\left(f\left(2\right)\right)=g\left(1\right)=3$$$$g\mathrm{o}f\left(3\right)=g\left(f\left(3\right)\right)=g\left(3\right)=2$$$$g\mathrm{o}f\left(4\right)=g\left(f\left(4\right)\right)=g\left(2\right)=1$$$$f\mathrm{o}g\left(x\right)=f\left(g\left(x\right)\right):x\in \{1,2,3,4\}$$$$f\mathrm{o}g\left(1\right)=f\left(g\left(1\right)\right)=f\left(3\right)=3$$$$f\mathrm{o}g\left(2\right)=f\left(g\left(2\right)\right)=f\left(1\right)=4$$$$f\mathrm{o}g\left(3\right)=f\left(g\left(3\right)\right)=f\left(2\right)=1$$$$f\mathrm{o}g\left(4\right)=f\left(g\left(4\right)\right)=f\left(4\right)=2$$

Answered by Rasheed.Sindhi last updated on 11/Mar/18

$$g\mathrm{o}f$$$$\left[\begin{array}{ccccc}1& f& 4& g& 4\\ 2& f& 1& g& 3\\ 3& f& 3& g& 2\\ 4& f& 2& g& 1\end{array}\right]$$$$f\mathrm{o}g$$$$\left[\begin{array}{ccccc}1& g& 3& f& 3\\ 2& g& 1& f& 4\\ 3& g& 2& f& 1\\ 4& g& 4& f& 2\end{array}\right]$$

Commented by mondodotto@gmail.com last updated on 11/Mar/18

$$\mathrm{please}\mathrm{i}\mathrm{need}\mathrm{more}\mathrm{explaination}\mathrm{about}\mathrm{this}\mathrm{method},\mathrm{i}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{understand}\mathrm{anything}$$

Commented by Rasheed.Sindhi last updated on 12/Mar/18

$$\left[\begin{array}{ccccc}x& f& f\left(x\right)& g& g\left(f\left(x\right)\right)\\ 1& f& 4& g& 4\\ 2& f& 1& g& 3\\ 3& f& 3& g& 2\\ 4& f& 2& g& 1\end{array}\right]$$$$\mathrm{I}\mathrm{have}\mathrm{added}\mathrm{a}\mathrm{guide}-\mathrm{row}\mathrm{for}\mathrm{clarification}.$$$$\mathrm{Middle}\mathrm{column}\mathrm{has}\mathrm{two}\mathrm{roles}:{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{output}$$$$\mathrm{of}f\mathrm{and}\mathrm{input}\mathrm{of}g.$$$$\mathrm{In}\mathrm{the}\mathrm{question}\mathrm{the}\mathrm{function}\mathrm{is}\mathrm{defined}$$$$\mathrm{by}\mathrm{ordered}\mathrm{pairs}.\mathrm{First}\mathrm{element}\mathrm{is}\mathrm{input}$$$$\mathrm{of}\mathrm{the}\mathrm{function}\mathrm{and}\mathrm{the}\mathrm{second}\mathrm{is}\mathrm{output}$$$$\mathrm{which}\mathrm{is}\mathrm{also}\mathrm{called}\mathrm{image}\mathrm{under}\mathrm{the}\mathrm{function}.$$$$(\mathrm{x},\mathrm{y})\in f\mathrm{may}\mathrm{also}\mathrm{be}\mathrm{written}\mathrm{x}f\mathrm{y}$$$$\mathrm{x}:\mathrm{input}\mathrm{of}f,\mathrm{y}:\mathrm{output}\mathrm{of}f$$$$\mathrm{y}\mathrm{is}\mathrm{also}\mathrm{called}\mathrm{image}\mathrm{of}\mathrm{x}\mathrm{under}f\mathrm{denoted}$$$$\mathrm{by}f\left(\mathrm{x}\right).$$

Commented by mondodotto@gmail.com last updated on 12/Mar/18

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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