Question

Find (h o h)(x) for the function h(x)= Vx+1 and simplify.

(h oh)(x)=
(Simplify your answer. Type an exact answer, using radicals as needed.)

Answer 1

The composition of the function h(x) with itself, denoted as (h ∘ h)(x), is √(√x + 1 + 1). This expression is a nested radical and cannot be simplified further without additional information.

Step-by-step explanation:

To find (h \circ h)(x) for the function h(x) = \sqrt{x + 1}, we need to evaluate the function h at the result of the function h(x). This means we will substitute h(x) back into itself.

First, compute h(x):

• h(x) = \sqrt{x + 1}

Then, compute h(h(x)):

• h(h(x)) = h(\sqrt{x + 1})
• = \sqrt{\sqrt{x + 1} + 1}

Now we have the composition of h with itself, which is:

(h \circ h)(x) = \sqrt{\sqrt{x + 1} + 1}

We cannot simplify this expression any further as it stands, since it's a nested radical and does not reduce to a simpler algebraic form without further context.