# checking whether $\log(x+1):(0,+\infty)\to (0,+\infty)$ is a function, then whether it is onto or 1-1 or both

$f:\mathbb{R}_+\to \mathbb{R}_+, f(x)=\log(x+1)$

How to start? Should i start computing $f(1), f(2) ....$ and then plotting them on the graph

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Plotting a graph of the function will certainly give you some good intuition. Can you write down an inverse to your function? Do you know why this would help? –  Edward Hughes Nov 9 '12 at 16:52
How do you define $\log$? As the inverse of $10^x$? I also think the title should be changed to "checking if $\log(x+1):(0,+\infty)\to (0,+\infty)$ is onto or 1-1 or both" –  Nameless Nov 9 '12 at 16:54
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## 1 Answer

Basically we have a set of positive real numbers as the domain and same for codomain. It is certainly a one one function as in log graph every value of x will give a unique y value.(Plot and SEE!) This function will also be onto as all real numbers on the x axis will give a different y value as the graph is not symmetrical and is always increasing .So also onto. Hope you get the idea :)

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