Answer to Question #147705 in Calculus for zahra

Question

Determine whether f is 1-1 by examining sign of f'(x)
f(x)= x/x+1

Answer 1

$f(x)=\frac{x}{x+1}$

$f'(x)=\frac{x+1-x}{(x+1)^2}=\frac{1}{(x+1)^2}$

Since f'(x) > 0 for all x except x=–1 the function is one-to-one.

The domain of f(x) is all x except x=–1, so the function is one-to-one on its domain.