If `f: Rvec` is defined by `f(x) = 3x – 5` Prove that `f` is a bijection. Also, find the inverse of `fdot`

Explanation

`{P}({x})=3 {x}-5`


Let `{y}=3 {x}-5 Rightarrow 3 {x}={y}+5`


`{x}=({y}+5) / 3`


Let `g(y)=frac{y+5}{3}`


Now `g circ f(x)=g[(f(x)]=g(3 x-5)`


also `f circ g(y)=frac{3 x-5+5}{3}=x[g(y)]=f[frac{y+5}{3}]`


Thus `g circ f=3(frac{y+5}{3})-5=y+5-5=y`


`f` and `g` are bijections and inverse to each other.


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