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Suppose $f_{\alpha}\::\:[0,1]\rightarrow[0,1],\:-1<\alpha<\infty$ is given by

$$f_{\alpha}(x)=\dfrac{(\alpha+1)x}{\alpha x+1}.$$

Then $f_{\alpha}$ is

  1. A bijective (one-one and onto) function.
  2. A surjective (onto) function.
  3. An injective (one-one) function.
  4. We can not conclude about the type.
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