Let `f: RvecR` be any function. Also `g: RvecR` is defined by `g(x)=|f(x)|` for all `xdot` Then is Onto if `f` is onto One-one if `f` is one-one Continuous if `f` is continuous None of these

Options

A. onto if f is onto
B. one-one if f is one-one
C. continuous if f is continuous
D. None of these

Answer

C

Explanation

(a) Since g(x) = `|f(x)|`
`therefore" "g(x) ge 0`
`therefore" Range of "g ne R". Hence, is not onto"`.
(b) If we take `f(x)=x`, then f is one-one but `|f(x)|=|x|` is not one-one.
(c) If f(x) is continuous then `|f(x)|` is also continuous.