What is the range of 2+arctan(x-1) ?

The range of 2+arctan(x-1) is -pi/2+2<f(x)< pi/2+2

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range of 2+arctan(x-1)

range

2 + arctan (x - 1)

- \frac{π}{2} + 2 < f (x) < \frac{π}{2} + 2

Interval Notation

(- \frac{π}{2} + 2, \frac{π}{2} + 2)

Solution steps

The range of the basic

arctan

function is

- \frac{π}{2} < arctan (x - 1) < \frac{π}{2}

- \frac{π}{2} < arctan (x - 1) < \frac{π}{2}

Add to the edges of the range:

2

- \frac{π}{2} + 2 < arctan (x - 1) + 2 < \frac{π}{2} + 2

Therefore the range is

- \frac{π}{2} + 2 < f (x) < \frac{π}{2} + 2

What is the range of 2+arctan(x-1) ?
The range of 2+arctan(x-1) is -pi/2+2<f(x)< pi/2+2