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

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Answer 1 · 2018-04-11T12:09:03

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

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

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]

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