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Question

Let $$f: {1,3,4} \rightarrow {1,2,5}$$ and $$g: {1,2,5}\rightarrow {1,3}$$ be given by $$f={(1,2), (3,5), (4,1)}$$ and $$g= {(1,3), (2,3), (5,1)}$$. Write down $$gof$$.


Solution

The function $$f: {1,3,5}\rightarrow {1,2,5}$$ and $$g:{1,2,5} \rightarrow {1,3}$$ are defined as

$$f={(1,2), (3,5), (4,1)}$$ and $$g= {(1,3), (2,3), (5,1)}$$

$$gof(1)=g(f(1))=g(2)=3 $$    as   $$[f(1)=2$$ and $$g(2)=3]$$

$$gof(3)=g(f(3))=g(5)=1 $$   as  $$[f(3)=5$$ and $$g(5)=1]$$

$$gof(4)=g(f(4))=g(1)=3$$    as  $$[f(4)=1$$ and $$g(1)=3]$$

$$\therefore gof ={(1,3),(3,1),(4,3)}$$

Mathematics
RS Agarwal
Standard XII

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