F^-1(x)=-1/2x+9

Solution for F^-1(x)=-1/2x+9 equation:

^-1(F)=-1/2F+9

We move all terms to the left:

^-1(F)-(-1/2F+9)=0


Domain of the equation: 2F+9)!=0

F∈R


We add all the numbers together, and all the variables

-1F-(-1/2F+9)=0

We get rid of parentheses

-1F+1/2F-9=0

We multiply all the terms by the denominator


-1F*2F-9*2F+1=0

Wy multiply elements

-2F^2-18F+1=0

a = -2; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-2)·1
Δ = 332
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{83}}{2*-2}=\frac{18-2\sqrt{83}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{83}}{2*-2}=\frac{18+2\sqrt{83}}{-4}
$