Find the derivative of `y = log_2 6x`.

Options

A. injective only
B. both injective as well as surjective
C. not injective but it is surjective
D. neither injective nor surjective

Answer

D

Explanation

We have, `f(x)=(|x-1|)/(x)={(-((x-1))/(x)", if "0 lt x le 1),((x-1)/(x)", if " x gt 1):}`
`={((1)/(x)-1", if "0 lt x le 1),(1-(1)/(x)", if " x gt 1):}`
Now, let us draw the graph of y=f(x)
Note that when ` x to 0, " then " f(x) to oo,` when x=1, then f(x) = 0, and when `x to oo, " then " f(x) to 1`

Clearly, f(x) is not injective because if `f(x) lt 1`, then f is many one, as shown in figure.
Also, f(x) is not surjective because range of f(x) is `[0,oo]` and but in problem co-domain is `(0,oo),` which is wrong.
`therefore f(x)` is neither injective nor surjective