Question

find the expression for: (f(x+h))-(f(x)))/h given: f(x)=sqrt(x-1) hint:rationalize the numerator

simplify far enough that plugging in h = 0 would be allowed

Answer 1

(f(x+h) - f(x)(/h = (√(x+h-1)-√(x-1))/h

Now multiply top and bottom by the conjugate, and you have

(√(x+h-1)-√(x-1))(√(x+h-1)+√(x-1))/(h(√(x+h-1)+√(x-1)))
= ((x+h-1)-(x-1))/(h(√(x+h-1)+√(x-1)))
= h/(h(√(x+h-1)+√(x-1)))
= 1/(√(x+h-1)+√(x-1))