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Let f be a function from R to R such tha...

Let `f` be a function from `R` to `R` such that `f(x)=cos(x+2)` . Is `f` invertible? Justify your answer.

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Injectivity:

Let `x` and `y` be two elements in the domain (R), such that

`f(x)=f(y) `

`Rightarrow cos (x+2)=cos (y+2) `

`Rightarrow x+2=y+2 text { or } x+2=2 pi-(y+2) `

`Rightarrow x=y text { or } x+2=2 pi-y-2 `

`Rightarrow x=y text { or } x=2 pi-y-4`

...
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