What is the inverse of f(x)=-2sin(x+pi/3)+sqrt(2) ?

The inverse of f(x)=-2sin(x+pi/3)+sqrt(2) is arcsin(-(x-sqrt(2))/2)-pi/3

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inverse of f(x)=-2sin(x+pi/3)+sqrt(2)

inverse

f (x) = - 2 sin (x + \frac{π}{3}) + 2

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

Solution steps

Solve for

sin (x + \frac{π}{3}), y = - 2 sin (x + \frac{π}{3}) + 2

sin (x + \frac{π}{3}) = - \frac{y - 2}{2}

sin (a) = b \Rightarrow a = arcsin (b)

x + \frac{π}{3} = arcsin (- \frac{y - 2}{2})

Solve for

x, x + \frac{π}{3} = arcsin (- \frac{y - 2}{2})

arcsin (- \frac{y - 2}{2}) - \frac{π}{3}

Substitute

y = x

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

What is the inverse of f(x)=-2sin(x+pi/3)+sqrt(2) ?
The inverse of f(x)=-2sin(x+pi/3)+sqrt(2) is arcsin(-(x-sqrt(2))/2)-pi/3