Please help me find the inverse function of this function 40x^2 - 40x + 5?

Answer 1

even functions don't have inverses unless you restrict the domain.
y = 40x² - 40x + 5
y = 40(x² - x + 1/8)
y = 40(x² - x + 1/4) - 40(1/8)
y = 40(x - 1/2)² - 5
y + 5 = 40(x - 1/2)²
(y + 5)/40 = (x - 1/2)²
±√[(y + 5)/40] = x - 1/2
x = 1/2 ± √[(y + 5)/40]
and here, for a given value of y, you get 2 values of x, so the inverse is not a function.