Question

find the inverse function of
y = 2x^2 - 8x

Answer 1

\[2x ^{2}-8x\]

Answer 2

the answer (i think) should be \[(8+\sqrt{64+8x})/4\] through use of quadratic equation and solving for "root" but i want to know why...

Answer 3

To find the inverse function, u must make x the subject of the equation.
y = 2x^2 - 8x

so, start by factorising,
y= 2[x^2 -4x]

then note that (x-2)^2 = x^2 -4x+4, note that it is similar to the top, just missing the variable +4 so we go ahead to add that in,
y= 2[x^2 -4x +4 -4] (note, u must put in +4 and -4 to make the eqn still equal.)
y= 2[ (x-2)^2 -4]
now u can easily arrange it to make x the subject,

(y/2) +4 = (x-2)^2
\[\pm \sqrt{y/2 +4}=x-2 \]
\[x=2\pm \sqrt{y/2+4}\]
Interchange both x and y,
\[y=2\pm \sqrt{x/2+4}\]
which is equal to the ans u have, just more simplified.

Answer 4

thank you!!!

Answer 5

Np!