What is the range of f(x)=arcsin(x-4)-pi/3 ?

The range of f(x)=arcsin(x-4)-pi/3 is -(5pi)/6 <= f(x)<= pi/6

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range of f(x)=arcsin(x-4)-pi/3

range

f (x) = arcsin (x - 4) - \frac{π}{3}

- \frac{5 π}{6} \leq f (x) \leq \frac{π}{6}

Interval Notation

[- \frac{5 π}{6}, \frac{π}{6}]

Solution steps

The range of the basic

arcsin

function is

- \frac{π}{2} \leq arcsin (x - 4) \leq \frac{π}{2}

- \frac{π}{2} \leq arcsin (x - 4) \leq \frac{π}{2}

Add to the edges of the range:

- \frac{π}{3}

- \frac{5 π}{6} \leq arcsin (x - 4) - \frac{π}{3} \leq \frac{π}{6}

Therefore the range is

- \frac{5 π}{6} \leq f (x) \leq \frac{π}{6}

What is the range of f(x)=arcsin(x-4)-pi/3 ?
The range of f(x)=arcsin(x-4)-pi/3 is -(5pi)/6 <= f(x)<= pi/6