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If f:[0,oo) to [0,1), " and " f(x)=(x)/...

If ` f:[0,oo) to [0,1), " and " f(x)=(x)/(1+x)` then check the nature of the function.

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To analyze the function \( f: [0, \infty) \to [0, 1) \) defined by \( f(x) = \frac{x}{1+x} \), we will check if the function is one-to-one (injective) and onto (surjective). ### Step 1: Check if the function is one-to-one (injective) To determine if the function is one-to-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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