# Consider the function #f(x)=1/(x-2)#, then how do you simplify f(f(x))?

[ f(f(x)) = \frac{1}{\frac{1}{x-2} - 2} ]

Combine the fractions in the denominator:

[ f(f(x)) = \frac{1}{\frac{1 - 2(x - 2)}{x - 2}} ]

Simplify further:

[ f(f(x)) = \frac{1}{\frac{-2x + 5}{x - 2}} ]

Invert and multiply:

[ f(f(x)) = \frac{1}{-2x + 5} ]

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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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