The function `f:[0,\ oo)->R` given by `f(x)=x/(x+1)` is (a) one-one and onto (b) one-one but not onto (c) onto but not one-one (d) neither one-one nor onto

Explanation

To determine whether the function \( f: [0, \infty) \to \mathbb{R} \) given by \( f(x) = \frac{x}{x+1} \) is one-one and/or onto, we will analyze the function step by step.

### Step 1: Check if the function is one-one (injective)

To check if the function is one-one, we need to show that if \( f(x_1) = f(x_2) \), then \( x_1 = x_2 \).

1. Assume \( f(x_1) = f(x_2) \).
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