What is the range of arccos(x-1)+pi/2 ?

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

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range of arccos(x-1)+pi/2

range

arccos (x - 1) + \frac{π}{2}

\frac{π}{2} \leq f (x) \leq π + \frac{π}{2}

Interval Notation

[\frac{π}{2}, π + \frac{π}{2}]

Solution steps

The range of the basic

arccos

function is

0 \leq arccos (x - 1) \leq π

0 \leq arccos (x - 1) \leq π

Add to the edges of the range:

\frac{π}{2}

\frac{π}{2} \leq arccos (x - 1) + \frac{π}{2} \leq π + \frac{π}{2}

Therefore the range is

\frac{π}{2} \leq f (x) \leq π + \frac{π}{2}

e x t re m e f (x) = x^{4} - 8 x^{3} + 7

d o main f (x) = \frac{1}{1 + x}

f (x) = - x^{2} + 4 x - 3

in v erse f (x) = 2 + \frac{1}{3} (x - 5)^{2}

am pl i t u d e \frac{1}{2} cos (2 x)

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