求反函数 f(x)=(x^{1/4}-1)^5

解答

求反函数

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

x^{\frac{4}{5}} + 4 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} + 4 5 x + 1

求解步骤

y = (x^{\frac{1}{4}} - 1)^{5}

用

y

替代

x

x = (y^{\frac{1}{4}} - 1)^{5}

求解

y, x = (y^{\frac{1}{4}} - 1)^{5}

x^{\frac{4}{5}} + 4 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} + 4 5 x + 1

a sy m pt o t es 1 + \frac{1}{x}

in f l ec t i o n f (x) = - \frac{1}{10} x^{5} + 5 x^{3}

cr i t i c a l f (x) = x^{\frac{11}{5}} + x^{\frac{6}{5}}

p a r i t y f (x) = x x + 5

a sy m pt o t es y = \frac{( 6 x + 1 )}{( 3 x - 5 )}