# What is the inverse function of #f(x)=1/(1+x)#. How inverse functions appear in graph?

Please see below.

graph{1/(1+x) [-10, 10, -5, 5]}

graph{(1+x)/x [-10, 10, -5, 5]}

graph{(y-x)(y-1/(1+x))(y+1-1/x)=0 [-10, 10, -5, 5]}

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See below

We can express this as

So:

This probably looks a bit intimidating, because it includes a lot of simplifying to make the differentiation easier.

Hope it helps though.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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