Which one of the following functions is one-one?

Options

A. `f:R to R" given by "f(x)|x-1|"for all "x in R`
B. `g:[-pi//2,pi//2] in R` is given by:
`g(x)=|sin x|"for all "x in[-pi//2,pi//2]`
C. `h:[-pi//2,pi//2] in R` is given by
`h=(x)=sin x" for all "x in [-pi//2, pi//2]`
D. `phi: R to R "given by" f(x)=x^(2)-4"for all x " inR`

Answer

C

Explanation

The graphs of f,g,h and `phi` are as shown below: It is evident from these graphs that `h:[-pi//2,pi//2] to R` given by h(x)=sin x is the one-one and all other functions are many-one as it is possible to draw horizontal line cutting or interescting the curves represented by them at more than one point.