Identify the type of the function `f:R to R,`
`f(x)=e^(x^(2))+cosx.`

Answer

many-one,into

Explanation

`f(x)=e^(x^(2))+cosx`
Clearly, `f(1)=f(-1),f(2)=f(-2)` etc.
So, `f(x)` is many-one.
Range of `e^(x^(2))` is `[1,oo)` and range of ` cos x " is " [-1,1].`
Thus `f(x)` does not take negative values.
Hence `f(x)` is into.