Calculus Homework

Question

Consider the function f(x) = 2x + 5 / √ x^2 − 1 . Find f(5), f(a), f(x + h).

Answer 1

For f(x) = (2x+5)/[√(x²) − 1]:

f(5) = (2(5)+5)/[√(5²) − 1] or 15/[5 − 1] or 15/4 or 3 + 3/(5 − 1).

f(a) = (2a+5)/[√(a²) − 1] or (2a+5)/[a − 1] or 2 + 7/[a − 1].

f(x+h) = (2(x+h)+5)/[√{(x+h)²} − 1] or (2x+2h+5)/(x+h−1) or 2 + 7/(x+h−1).