求反函数 f(x)=tan(x+pi/2)-1

解答

求反函数

f (x) = tan (x + \frac{π}{2}) - 1

arctan (x + 1) - \frac{π}{2}

求解步骤

求解

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)

求解

x, x + \frac{π}{2} = arctan (y + 1)

arctan (y + 1) - \frac{π}{2}

替代

y = x

arctan (x + 1) - \frac{π}{2}

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

in v erse - x + 8

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

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

in v erse 8 x + 7