Question

How do you find the range and domain of `(1/2)(arctan x)`?

Answer 1

Domain : `x|(-oo,oo)`
Range: `f(x)|(-pi/4,pi/4)`

Explanation:

`f(x)=1/2*tan^-1 x`

Domain of `tan^-1 x` is any real value i.e `x|(-oo,oo)`

Range of `tan^-1 x` is `f(x)|(-pi/2,pi/2)`

Domain of `(1/2)tan^-1 x` is `x|(-oo,oo)`

Range of `(1/2)tan^-1 x` is `f(x)|(-pi/4,pi/4)`

graph{1/2*arctan(x) [-10, 10, -5, 5]} [Ans]