SOLUTION: Find the inverse for the function F (x)=x^2-x-6 with domain x greater or equal to 1/2, × is real numbers If no inverse exists explain why

Algebra ->  Square-cubic-other-roots -> SOLUTION: Find the inverse for the function F (x)=x^2-x-6 with domain x greater or equal to 1/2, × is real numbers If no inverse exists explain why      Log On


   

Question 971360: Find the inverse for the function
F (x)=x^2-x-6 with domain x greater or equal to 1/2, × is real numbers
If no inverse exists explain why
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
F%28x%29=x%5E2-x%2B1%2F2-1%2F2-6
F%28x%29=%28x-1%2F4%29%5E2-6%261%2F2
F%28x%29=%28x-1%2F4%29%5E2-13%2F2

Inverse would be %28y-1%2F4%29%5E2-13%2F2=x
%28y-1%2F4%29%5E2=13%2F2%2Bx
y-1%2F4=0%2B-+sqrt%2813%2F2%2Bx%29
y=1%2F4%2B-+sqrt%2813%2F2%2Bx%29-------Not finished.

Domain for F was x%3E=1%2F2. Now, the RANGE of y is y%3E=1%2F2; and the upper branch of y is what is wanted:

highlight%28y=1%2F4%2Bsqrt%2813%2F2%2Bx%29%29;
Also the needed domain for x is x%3E=-13%2F2 to stay within real numbers.