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

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

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

inverse

f (x) = - tan (x + \frac{π}{3}) + 2

arctan (2 - x) - \frac{π}{3}

Solution steps

Solve for

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

tan (x + \frac{π}{3}) = 2 - y

tan (a) = b \Rightarrow a = arctan (b)

x + \frac{π}{3} = arctan (2 - y)

Solve for

x, x + \frac{π}{3} = arctan (2 - y)

arctan (2 - y) - \frac{π}{3}

Substitute

y = x

arctan (2 - x) - \frac{π}{3}

f (x) = \frac{x ^{2} - 1}{4}

f (x) = - x + 6

f (x) = x^{2} + 16

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