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  • Need solution for RD Sharma Maths Class 12 Chapter Function Exercise 2.2 Question 10.

Need solution for RD Sharma Maths Class 12 Chapter Function Exercise 2.2 Question 10.

Answers (1)

Answer : h\; o(g\; o\; f)=(h\; o\; g)o\; f

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: N \rightarrow N, g: N \rightarrow N, h: N \rightarrow R defined as

             \begin{array}{r} f(x)=2 x \\ g(y)=3 y+4 \\ h(z)=\sin z \\ \text { All } x, y, z \in N \end{array}

Solution :

             \begin{aligned} h \circ(g \circ f)(x)=& h(g \circ f(x))=h(g(f(x))) \\ &=h(g(2 x))=h(3(2 x)+4) \\ &=h(6 x+4) \\ &=\sin (6 x+4) \quad \forall x \in N \end{aligned}

Similarly,

\begin{aligned} ((h \circ g) \circ f)(x) &=(h \circ g)(f(x)) \\ &=(h \circ g)(2 x) \\ &=h(g(2 x))=h(3(2 x)+4) \end{aligned}

                                 =h(6x+4)=\sin(6x+4) \; \; \; \; \; \; \; \forall x\; \epsilon \; N

This shows,   h\; o(g\; o\; f)=(h\; o\; g)o\; f

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