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  • Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 1 Sub question (ii) maths textbook solution.

Please solve RD Sharma Class 12 Chapter Functions Exercise 2.3 Question 1 Sub question (ii) maths textbook solution.

Answers (1)

Answer :

\begin{aligned} &g \circ f(x)=\cos x^{2} \\ &f \circ g(x)=\cos ^{2} x \end{aligned}

Hint : Domain of f and domain g = R

          Range of f=(0,\infty )

          Range of g g=(-1,1 )

    \therefore Range of f \subset domain of g

\Rightarrow \; \; \; \; \; \; \; \; g\; o\; f exists

      and Range of g \subset domain of f

\Rightarrow \; \; \; \; \; \; \; \; f\; o\; g exists

Given : Here given that

             f(x)=x^{2}\; \text {and}\; g(x)=\cos x

Solution :

Here first we will find out g\; o\; f,

We have,

\begin{array}{r} f(x)=x^{2} \text { and } g(x)=\cos x \\ \therefore g \circ f(x)=g\{f(x)\} \\ =g\left\{x^{2}\right\} \\ =\cos x^{2} \end{array}

and again for f\; o\; g

              \begin{aligned} &\therefore \operatorname{fog}(x)=f\{g(x)\} \\ &\qquad \begin{aligned} &=f\{\cos x\} \\ &=\cos ^{2} x \end{aligned} \end{aligned}

NOTE : f\; o\; g is defined only when range (g)\subseteq \text {dom}\; (f) \; \text {and dom}\;f\; o\; g=\text {dom}(g) .

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