What is the inverse of ax^2-4x+2a ?

The inverse of ax^2-4x+2a is (2+sqrt(-a(-x+2a)+4))/a ,(2-sqrt(-a(-x+2a)+4))/a

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inverse of ax^2-4x+2a

inverse

a x^{2} - 4 x + 2 a

\frac{2 + - a ( - x + 2 a ) + 4}{a}, \frac{2 - - a ( - x + 2 a ) + 4}{a}

Solution steps

y = a x^{2} - 4 x + 2 a

Replace

x

with

y

x = a y^{2} - 4 y + 2 a

Solve for

y, x = a y^{2} - 4 y + 2 a

\frac{2 + - a ( - x + 2 a ) + 4}{a}, \frac{2 - - a ( - x + 2 a ) + 4}{a}

f (x) = (x^{2} - 1) (x^{2} - 4) (x^{2} - 9)

f (x) = \frac{x + 5}{x - 3}

\frac{3}{x ^{2} - 4}

f (x) = (x + 3)^{5}

(4, - 5), (8, 7)

What is the inverse of ax^2-4x+2a ?
The inverse of ax^2-4x+2a is (2+sqrt(-a(-x+2a)+4))/a ,(2-sqrt(-a(-x+2a)+4))/a