Show that the function `f : R to R : f(x) =3-4 x` is one-one onto and – InterviewSolution

InterviewSolution

1.	Show that the function `f : R to R : f(x) =3-4 x` is one-one onto and hence bijective.
Answer» We have `f(x_(1)) =f(x_(2)) rArr 3 -4x_(1) =3 - 4x_(2)` `rArr -4x_(1) =-4x_(2) rArr x_(1) =x_(2)` `:.` f is one-one. Now let `y= 3-4x.` Then `x= ((3-y))/(4)` Thus for each `y in R` (codomain of f) there exists `x=((3-y))/(4) in R` Such that `f(x) = ((3-y)/(4)) ={ 3-4 . ((3-y)/(4))} =3 -(3-y) =y` Thus shows that every elements in codomain of f has its pre-image in dom (f). `:. ` f is onto. `Hence the given function is bijective .

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