Find the quotient of the identity function by the modulus function. – InterviewSolution

InterviewSolution

1.	Find the quotient of the identity function by the modulus function.
Answer» Let `f:RtoR:f(x)=xandg:RtoR:g(x)=\|x\|` be the identity function and the modulus function respectively. Now, dom `((f)/(g))="dom "(f)nn"dom "(g)-{x:g(x)=0}` and `{x:g(x)=0}={x:""\|x\|=0}={0}`. `:."dom "((f)/(g))=[RnnR-{0}]-{0}=R-{0}` So, `(f)/(g):R-{0}toR:((f)/(g))(x)=(f(x))/(g(x))=(x)/(\|x\|)={{:(1",when "xgt0),(-1",when "xlt0):}` Hence, `((f)/(g))(x)={{:(1",when "xgt0),(-1",when "xlt0):}`.

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