Question

show that f:R-{2} to R-{0} given by f(x)=1/x-2 is bijective.Also find f inverse
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Answer 1

Step-by-step explanation:

Given, function f:R→R such that f(x)=1+x2, 

Let A and B be two sets of real numbers.

Let x1,x2∈A such that f(x1)=f(x2).

⇒1+x12=1+x22⇒x12−x22=0⇒(x1−x2)(x1+x2)=0

⇒x1=±x2. Thus f(x1)=f(x2) does not imply that x1=x2.

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