Which of the following functions from `A={x in R :-1lt=xlt=1}` to itself are bijections? `f(x)=|x|` (b) `f(x)=sin(pix)/2` (c) `f(x)=sin(pix)/4` (d) none of these

Explanation

(A) As we know that
`(−1)=∣−1∣=1`

And `h(1)=∣1∣=1`

`⇒ −1` and `1` have the same images

So, h is not a bijection.


(B) Range `=[sin(−π/2​),sin(π/2​)]=[−1,1]=A`
So, g is a bijection.


(C) Range `=[sin(-π/4​),sin(π/4​)]=[−1,1]=A`

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