# Discuss what you believe to be the domain which will make y= arcos(x) and y = arctan(x), functions.

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### 1 Answer

`y=cos^(-1)(x)` (i)

since

`x=cos(y)` is one to one and onto if `y in[0,pi]` .

Thus (i) is function if `x in[-1,1] and yin[0,pi]`

`y=tan^(-1)(x)` (ii)

since

`x=tan (y)` is one to one and onto if `yin(-pi/2,pi/2)`

Thus (ii) is function if `x in (-oo,oo) and yin(-pi/2,pi/2)`