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

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

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inverse of f(x)=arctan(x+pi/2)

inverse

f (x) = arctan (x + \frac{π}{2})

tan (x) - \frac{π}{2}

Solution steps

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

x + \frac{π}{2} = tan (y)

Solve for

x, x + \frac{π}{2} = tan (y)

tan (y) - \frac{π}{2}

Substitute

y = x

tan (x) - \frac{π}{2}

f (x) = 2^{x + 4} - 5

2 x

2 x^{3} - 6 x

f (x) = - 3 x^{2} + 4

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