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Please solve RD Sharma class 12 chapter Functions exercise 2.2 question 1 sub question (iv) maths textbook solution.

Answers (1)

Answer : f\; o\; g=\left | x \right | \; \text {and} \; g\; o\; f=\left | x \right |

Hint : g\; o\; f means f(x) function is in g(x) function

         f\; o\; g means g(x) function is in f(x) function

Given : f(x)=x

            g(x)=\left | x \right |

Solution :

Since f:R\rightarrow R\; \text {and}\; g:R\rightarrow R

          f\; o\; g:R\rightarrow R\; \text {and}\; g\; o\; f:R\rightarrow R

Now,  g\; o\; f (x)=g(f(x))


          g\; o\; f \left ( x \right )= \left | x \right |

Similarly ,

        f\; o\; f (x)=f(g(x))

                            =f \left | x \right |

        f\; o\; g(x)= \left | x \right |

Hence, f\; o\; g= \left | x \right |\; \text {and}\; g\; o\; f=\left | x \right |


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