SOLUTION: If f(x) = √x^2-1 and g(x) = √x-1 which expression represents f(x)/g(x) for x>1?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: If f(x) = √x^2-1 and g(x) = √x-1 which expression represents f(x)/g(x) for x>1?      Log On


   

Question 888276: If f(x) = √x^2-1 and g(x) = √x-1 which expression represents f(x)/g(x) for x>1?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%5E2+-+1%29+%2F+sqrt%28x-1%29 = sqrt%28%28x%5E2-1%29%2F%28x-1%29%29 = sqrt%28%28x-1%29%28x%2B1%29%2F%28x-1%29%29 = sqrt%28x%2B1%29

following is the graph of the equation of sqrt%28x%5E2+-+1%29+%2F+sqrt%28x-1%29

$$$

following is the graph of the equation of sqrt%28x%2B1%29

$$$

the first graph doesn't allow values of x = 1 because that would make the denominator equal to 0 and the function would be undefined.

the first graph also doesn't allow values of x <1 because that would make the numerator the squart root of a negative number which is also undefined in the real number system.

the second graph goes to 0 because x+1 will be positive for values less than 1 of x but greater than or equal to 0 and will also allows x = 1 because there is no denominator in that equation.

the 2 equations are equivalent except that once you eliminated the denominator by canceling it out, you can then get a defined solution at x = 1.