# How do you write # y = sqrt(sqrt(x) + 1)# as a composition of two simpler functions?

You can write ( y = \sqrt{\sqrt{x} + 1} ) as a composition of two simpler functions by breaking it down into its constituent parts. First, let's consider the innermost function:

- Let ( u = \sqrt{x} ).

Then, the original function becomes:

- ( y = \sqrt{u + 1} ).

Now, you can further decompose ( y ) in terms of ( u ):

- Let ( v = u + 1 ).

Then, the function becomes:

- ( y = \sqrt{v} ).

Combining these steps, you have:

- ( y = \sqrt{\sqrt{x} + 1} = \sqrt{\sqrt{x} + 1} ).

Thus, you have expressed ( y = \sqrt{\sqrt{x} + 1} ) as a composition of two simpler functions: ( u = \sqrt{x} ) and ( v = u + 1 ).

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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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