What is the inverse of f(x)=tan(x+pi/2)-1 ?

The inverse of f(x)=tan(x+pi/2)-1 is arctan(x+1)-pi/2

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inverse of f(x)=tan(x+pi/2)-1

inverse

f (x) = tan (x + \frac{π}{2}) - 1

arctan (x + 1) - \frac{π}{2}

Solution steps

Solve for

tan (x + \frac{π}{2}), y = tan (x + \frac{π}{2}) - 1

tan (x + \frac{π}{2}) = y + 1

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

x + \frac{π}{2} = arctan (y + 1)

Solve for

x, x + \frac{π}{2} = arctan (y + 1)

arctan (y + 1) - \frac{π}{2}

Substitute

y = x

arctan (x + 1) - \frac{π}{2}

f (x) = (x + 4)^{2} + 8

- x + 8

f (x) = 1 - e^{- 3 x}

f (x) = \frac{9 ( 1 ) - 3}{9 ( 1 ) + 7}

f (x) = \frac{4}{3} ln (4 x - \frac{1}{3}) - \frac{4}{5}

What is the inverse of f(x)=tan(x+pi/2)-1 ?
The inverse of f(x)=tan(x+pi/2)-1 is arctan(x+1)-pi/2