求反函数 f(x)=1+sin^2(x-e/2)

解答

求反函数

f (x) = 1 + sin^{2} (x - \frac{e}{2})

arcsin (x - 1) + \frac{e}{2}, arcsin (- x - 1) + \frac{e}{2}

求解步骤

求解

sin (x - \frac{e}{2}), y = 1 + sin^{2} (x - \frac{e}{2})

sin (x - \frac{e}{2}) = y - 1, sin (x - \frac{e}{2}) = - y - 1

sin (a) = b \Rightarrow a = arcsin (b)

x - \frac{e}{2} = arcsin (y - 1), x - \frac{e}{2} = arcsin (- y - 1)

求解

x, x - \frac{e}{2} = arcsin (y - 1)

求解

x, x - \frac{e}{2} = arcsin (- y - 1)

arcsin (y - 1) + \frac{e}{2}, arcsin (- y - 1) + \frac{e}{2}

替代

y = x

arcsin (x - 1) + \frac{e}{2}, arcsin (- x - 1) + \frac{e}{2}

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

in v erse 2 (x - 1)^{2} - 4

in v erse f (x) = \frac{x + 5}{2 - 7 x}

in v erse f (z) = \frac{z ^{2} - z}{z + 1}

in v erse f (x) = 4 (1 - x^{2})