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  • Provide solution for RD Sharma Maths Class 12 Chapter Functions Exercise 2.2 Question 2.

Provide solution for RD Sharma maths Class 12 Chapter Functions Exercise 2.2 Question 2.

Answers (1)

Answer : f\; o\; g= \left \{ (1,1),(3,1),(4,3),(5,3) \right \}

               g\; o\; f= \left \{ (3,3),(9,3),(12,9) \right \}

Hint : The set which contains all the elements of all the ordered pairs of relation R is known as the domain of the relation. The set            which contains all the second element, is known as the range of the relation.

Given : f=\left \{ (3,1),(9,3),(12,4) \right \}

              g=\left \{ (-1,-2),(-2,-4),(-3,-6),(4,8) \right \}

Prove : g\; o\; f and f\; o\; g are both defined

Solution :  f:\left \{ 3,9,12 \right \}\rightarrow \left \{ 1,3,4 \right \}\; \text {and}\; g:\left \{ 1,3,4,5 \right \}\rightarrow \left \{ 3,9 \right \}

Co-domain of f  is a subset of the domain g

So, g\; o\; f exist and g\; o\; f:\left \{ 3,9,12 \right \}\rightarrow \left \{ 3,9 \right \}

      (g\; o\; f)(3)=g(f(3))=g(1)=3

      (g\; o\; f)(9)=g(f(9))=g(3)=3

      (g\; o\; f)(12)=g(f(12))=g(4)=9

       g\; o\; f =\left \{ \left ( 3,3 \right ),\left ( 9,3 \right ),\left ( 12,9 \right ) \right \}

 Co-domain of g is subset of the domain of f.

So, f\; o\; g exist and f\; o\; g:\left \{ 1,3,4,5 \right \}\rightarrow \left \{ 3,9,12 \right \}

      (f\; o\; g)(1)=f(g(1))=f(3)=1

       (f\; o\; g)(3)=f(g(3))=f(3)=1

      (f\; o\; g)(4)=f(g(4))=f(9)=3

      (f\; o\; g)(5)=f(g(5))=f(9)=3

     f\; o\; g=\left \{ (1,1),(3,1),(4,3),(5,3) \right \}

Hence proved, g\; o\; f and f\; o\; g are both defined.

             f\; o\; g=\left \{ (1,1),(3,1),(4,3),(5,3) \right \} and

             g\; o\; f=\left \{ (3,3),(9,3),(12,9) \right \}

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