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Explain solution RD Sharma Class 12 Chapter Functions Exercise 2.2 Question 13 maths textbook solution.

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Answer : g\; o\; f is a one -one function.

Hint : one-one functions means every domain has a distinct image. If one-one is given for any function

        f(x) \text { as if } F\left(x_{1}\right)=F\left(x_{2}\right) \text { then } x_{1}=x_{2} \text { where } x_{1}, x_{2} \in \text { domains of } f(x)

Given : f:A\rightarrow B\; \text {and}\; g:B\rightarrow C one-one function

Solution :   

     \begin{aligned} &\text { Let, } x, y \in A \text { such that } \\ &g \circ f(x)=g \circ f(y) \\ &g(f(x))=g(f(y)) \end{aligned}

   f(x)=f(y)                                                               [ \because g is one - one ]

        x=y                                                                       [\because f is one - one]

g\; o\; f is a one - one function.

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