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

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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