Question

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

• A. Differentiable everywhere
• B. Continuous but not differentiable at x=0
• C. Not a continuous function
• D. None of these

Answer 1

Answer: (A)

Differentiable everywhere

Answer 2

The range of the function x³ is (–∞, ∞), and the range of f(x) is [0, ∞), f is clearly differentiable except possibly at the point x = 0.

Now, clearly by definition Rf′(0) = L f′(0) = 0

so that, f is differentiable at x = 0 and hence every where

Alternative solution:

Here f (x) =

so that f′ (x) =

⇒ the function is differentiable everywhere including x = 0