What is the range of pi-3arcsin(2x-1) ?

The range of pi-3arcsin(2x-1) is -(3pi)/2+pi<= f(x)<= (3pi)/2+pi

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range of pi-3arcsin(2x-1)

range

π - 3 arcsin (2 x - 1)

- \frac{3 π}{2} + π \leq f (x) \leq \frac{3 π}{2} + π

Solution steps

The range of the basic

arcsin

function is

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

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

Multiply the edges of the range by:

- 3

- \frac{3 π}{2} \leq - 3 arcsin (2 x - 1) \leq \frac{3 π}{2}

Add to the edges of the range:

π

- \frac{3 π}{2} + π \leq - 3 arcsin (2 x - 1) + π \leq \frac{3 π}{2} + π

Therefore the range is

- \frac{3 π}{2} + π \leq f (x) \leq \frac{3 π}{2} + π

y = - \frac{1}{3} x + 9

f (x) = t - 4

(x + 4)^{2} - 9

16 x - 20 y = 60

\frac{x + 8 + 2}{x + 2}

What is the range of pi-3arcsin(2x-1) ?
The range of pi-3arcsin(2x-1) is -(3pi)/2+pi<= f(x)<= (3pi)/2+pi