The question asks to identify which of the given functions is even ("парну" in Ukrainian). Let's solve it.

Step 1: Recall the definition of an even function.

A function $f(x)$ is called even if: $f(-x) = f(x)$ for all $x$. Geometrically, even functions are symmetric about the $y$-axis.

Step 2: Analyze each option.

• (A) $y = x + 5$: Substituting $-x$: $f(-x) = -x + 5 \neq x + 5$ This is not even.

• (B) $y = \cos(\cos x)$: Substituting $-x$: $f(-x) = \cos(\cos(-x)) = \cos(\cos x)$ Since $\cos(-x) = \cos(x)$, this function is even.

• (C) $y = \sin(\sin x)$: Substituting $-x$: $f(-x) = \sin(\sin(-x)) = \sin(-\sin x) = -\sin(\sin x)$ This is not even.

• (D) $y = \sqrt[4]{x}$: Substituting $-x$: $f(-x) = \sqrt[4]{-x}$ Since roots of negative numbers are undefined in the real numbers, this is not a valid even function.

• (E) $y = x^5$: Substituting $-x$: $f(-x) = (-x)^5 = -x^5 \neq x^5$ This is not even.

Step 3: Conclusion.

The correct answer is (B) $y = \cos(\cos x)$.

Would you like a detailed explanation of even vs odd functions or how to analyze similar problems? Here are five follow-up questions to expand on this topic:

1. What is the definition of an odd function, and how does it differ from an even function?
2. Can a function be both even and odd? Provide examples or explanations.
3. How can you test whether a function like $y = x^2 + 1$ is even or odd?
4. What are the graphical characteristics of even functions?
5. How does the periodicity of trigonometric functions like $\sin x$ and $\cos x$ relate to their symmetry?

Tip: Even functions are symmetric about the $y$-axis, so visualizing their graphs can often help confirm their symmetry properties!