SOLUTION: Find the inverse function of y = √(x^2-5x-6) I have tried doing: x = √(y^2-5y-6) x^2 = y^2-5y-6.......and couldn't isolate y from here. Thank-you for your time!

Algebra ->  Functions -> SOLUTION: Find the inverse function of y = √(x^2-5x-6) I have tried doing: x = √(y^2-5y-6) x^2 = y^2-5y-6.......and couldn't isolate y from here. Thank-you for your time!      Log On


   

Question 919876: Find the inverse function of y = √(x^2-5x-6)
I have tried doing:
x = √(y^2-5y-6)
x^2 = y^2-5y-6.......and couldn't isolate y from here.
Thank-you for your time!
Found 2 solutions by MathLover1, josgarithmetic:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+sqrt%28x%5E2-5x-6%29

x+=+sqrt%28y%5E2-5y-6%29

x%5E2+=+y%5E2-5y-6
++y%5E2-5y-x%5E2-6=0
++y%5E2-5y-%28x%5E2%2B6%29=0 use quadratic formula; note that a=1,b=-5, and c=-x%5E2-6%29



y+=+%285+%2B-+sqrt%28+25%2B4%28x%5E2%2B6%29+%29%29%2F2+

y+=+%285+%2B-+sqrt%28+25%2B4x%5E2%2B24+%29%29%2F2+

y+=+%285+%2B-+sqrt%284x%5E2%2B49%29%29%2F2+

y+=+%281%2F2%29%285+%2B-+sqrt%284x%5E2%2B49%29%29+
or
f%5E-1%28x%29=+%281%2F2%29%285+%2B-+sqrt%284x%5E2%2B49%29%29+


Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
The roles of domain and range are switched from function to inverse.
Your given functional-form equation to start with is the upper half of a parabola with a horizontal symmetry axis.
Try completing-the-square to have a better understanding of your given parabola.

x%5E2-5x-6%2B%285%2F2%29%5E2-%285%2F2%29%5E2
x%5E2-5x%2B%285%2F2%29%5E2-6-%285%2F2%29%5E2
%28x-5%2F2%29%5E2-6-25%2F4
%28x-5%2F2%29%5E2-24%2F4-25%2F4
%28x-5%2F2%29%5E2-49%2F4

Now, what you are starting with is highlight_green%28y=sqrt%28%28x-5%2F2%29%5E2-49%2F4%29%29.
The vertex for this given equation is (5/2,-49/4).
The shape is horizontal parabola.
DOMAIN: x values must be greater than 5/2.
RANGE: y values are greater than or equal to -49/4.

If you want to now use the simple method of just switching x and y roles in the given equation, you can; and just solve that for y; and remember you must choose the RIGHT-HAND branch of the function.