show that the function `f : R to R : f (x) =2x +3` is invertible and f – InterviewSolution

InterviewSolution

1.	show that the function `f : R to R : f (x) =2x +3` is invertible and find `f^(-1)`
Answer» Correct Answer - `f^(-1) (y)= (1)/(2) (y-3)` `f(x_(1)) =f(x_(2)) rArr 2x_(1) +3 =2x_(2)+3 rArr 2x_(1)=2x_(2) rArr x_(1)=x_(2)` `:. ` f is one-one If `y in R` then there exists `x=(y-3)/(2) in R` such that `f(x)= f((y-3)/(2)) ={2.((y-3))/(2)+3}=y` `:. ` f is onto. `y =f(x) rArr y =2x+3` `rArr x=(1)/(2) (y-3) rArr f^(-1) (y)=(1)/(2) (y-3)`

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