Math, asked by anwesh211104, 5 months ago

Find the quotient of the identity function by its reciprocal function, for all real numbers except zero.
A. x
B. 1/x
C. 2x
D. x^2​

Answers

Answered by mad210203
0

Given:

Identity function  f(x)=x

and Reciprocal function  g(x)=\frac{1}{x}

To find:

Quotient of identity function by Reciprocal function for all real numbers except Zero

Solution:

Identity function is  f(x)=x \,\forall \,x \in R  

and Reciprocal function is g(x)=\frac{1}{x}\,\forall \,x \in R-\{0\}

The Quotient of Identity function by Reciprocal function =\frac{f(x)}{g(x)}

                                                                                     =\frac{x}{\frac{1}{x} }

                                                                                     =x^{2}

Now for finding the domain of the function \frac{f(x)}{g(x)}=x^{2} :-

dom\{x^{2} \}= dom\,\{f(x)\} \,\cap \, dom\,\{g(x)\}

dom\,\{x^{2} \}=R\,\cap\,R-\{0\}=R-\{0\}

\therefore The quotient of Identity function by Reciprocal function is x^{2} \,\forall\,x\,\in\,R-\{0\}.

Similar questions