Question

一道反函数题已知函数f(x)=根号(ax+2) (a

Answer 1

函数f(x)的图像与y=x的图像交点

x = √(ax+2)

x^2 -ax -2 = 0

x 1= (a+√(a^2+8))/2 > 0

x 2= (a-√(a^2+8))/2 < 0

x = f(x) >= 0

only x1 is the root of the equation,

when x = (a+√(a^2+8))/2 , a < 0

ax + 2 = (a^2 +a√(a^2+8)) /2 +2 > 0, therefore,

函数f(x)的图像与y=x的图像有且仅有一个交点