quadric and parabola

Question

If f(x) = √x^2 -1 and g(x)=√x-1, which expression represents f(x)/g(x) for x>1.

 

a. √x

b. √x+1

c. √x-1

d. 1/√x+1

Answer 1

Hi again Christine;

If f(x) = √x^2 -1 and g(x)=√x-1, which expression represents f(x)/g(x) for x>1.

f(x) = √(x²-1)

This can be factored as...

f(x)=√(x+1)(x-1)

g(x)=√(x-1)

f(x)/g(x)=[√(x+1)(x-1)]/√(x-1)

√(x-1) cancels as it is in the numerator and denominator...

f(x)/g(x)=√(x+1)

Correct answer is b.