The function `f.RtoR" defined by "f(x)=(x^(2)+1)^(35)` for all `x""inR` is

Options

A. one-one but not onto
B. onto but not one-one
C. neither one-one nor onto
D. both one-one and onto

Answer

C

Explanation

`f(-1)=f(1)=2^(35)`
Here, two real numbers 1 and -1 have the same image.
So, the function is not one-one and let
`y=(x^(2)+1)^(35)`
`impliesx=sqrt((y)^(1//35)-1)`
Thus, every real number has no pre image. So the function is not onto.
Hence, the function is neither one-one nor onto.