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Need solution for RD Sharma Maths Class 12 Chapter Function Exercise 2.2 Question 8.

Answers (1)

Answer : f\; o\; g=g\; o\; f=I_{R}

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:R \rightarrow R and g:R \rightarrow R are defined by


Solution :

  \begin{aligned} &f \circ g(x)=f(g(x))=f(x-1) \\ &f \circ g(x)=x-1+1 \\ & f \circ g(x)=x=I_{R} \end{aligned}                                        .....(i)


 \begin{aligned} &g \circ f(x)=g(f(x))=g(x+1) \\ &g \circ f(x)=x+1-1 \\ &g \circ f(x)=x=I_{R} \end{aligned}                                      ..... (ii)

From equation (i) and (ii)

f\; o\; g=g\; o\; f=I_{R}

Hence proved : f\; o\; g=g\; o\; f=I_{R}

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