What is the inverse function of 2x^2-9x+14?

Question

What is the inverse function of 2x^2-9x+14?

Answer 1

first find the vortex

(2.25 , 3.875)

then

y = 2x² -9x + 14

change x<->y

x= 2y² -9y + 14

add -x to both side

0 = 2y² - 9y + 14 -x

solve for y using quadratic formula.

y  = 2.25 +- r (0.5x -1.9375)

there are 2 interval with 2 different inverse funktions

for x< 2.25  f ^-1 (x) = 2.25 - r (0.5x -1.9375)

for x>2.25   f ^-1 (x) = 2.25 + r (0.5x -1.9375)

  

Answer 2

The inverse function does not exist unless you specify a domain where the function is one to one

Answer 3

This is a quadratic equation that is not factorable as (x-a)(x-b) where a and b are integers.

The roots are complex.

If you can express x in terms of y

y=2x^2-9x+14, the solution is the inverse.

No inverse.