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

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

Answers (1)

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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