Find the difference quotient of f(x)=√(x-2)

Question

The difference quotient is DQf=f(x+h)-f(x)/h. x-2 is what is being square rooted.

Answer 1

D.Q. = [√(x+h-2) -  √(x-2)] / h

 

To simplify, one can multiply both top & bottom of this 'fraction' by the conjugate of the surd numerator; in this way, you will find that the new numerator is h and that will cancel the old h denominator, giving 

1 / [√(x+h-2) + √(x-2)]