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

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

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

inverse

f (x) = a + arctan (2 x + π)

\frac{tan ( x - a ) - π}{2}

Solution steps

Solve for

arctan (2 x + π), y = a + arctan (2 x + π)

arctan (2 x + π) = y - a

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

2 x + π = tan (y - a)

Solve for

x, 2 x + π = tan (y - a)

\frac{tan ( y - a ) - π}{2}

Substitute

y = x

\frac{tan ( x - a ) - π}{2}

f (x) = (e^{x})^{7} + 8

f (x) = - 4 x - 1 + 7

- 2 x - 8

\frac{x}{x - 1}

f (x) = \frac{6 x - 7}{2 x - 2}

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