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  • Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 11 Sub question (i) maths textbook solution.

Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 11 Sub question (i)  maths textbook solution.

Answers (1)

Answer : (f \circ f)(x)=\sqrt{\sqrt{x-2}-2}

Hint : Domain f=(2,\infty ) and Range (f)=(0,\infty )

Clearly, the range of (f) is not a subset of domain of f.

Given : Here f be a real function given by f(x)=\sqrt{x-2}

            Here we have to compute f\; \circ \; f

Solution :

We know that

\because Domain of  (f \circ f)=\{x: x \in \text { Domain of } f \text { and } f(x) \in \text { Domain }(f)\}

          \begin{aligned} &=\{x: x \in(2, \infty) \text { and } \sqrt{x-2} \in(2, \infty) \\ &=\{x: x \in(2, \infty) \text { and } \sqrt{x-2} \geq 2\} \\ &=\{x: x \in(2, \infty) \text { and } x-2 \geq 4\} \\ &=\{x: x \in(2, \infty) x \geq 6 \\ &=(6, \infty) \end{aligned}

Now, 

\begin{aligned} (f \circ f)(x) &=f(f(x)) \\ &=f(\sqrt{x-2}) \\ &=\sqrt{\sqrt{x-2}-2} \\ \therefore f \circ f:(6, \infty) \rightarrow R \end{aligned}

Hence, (f \circ f)(x)=\sqrt{\sqrt{x-2}-2}

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