To determine whether the functions $f(x) = \frac{2x+1}{10}$ and $g(x) = \frac{10}{2x-1}$ are inverses, we can check if $f(g(x)) = x$ and $g(f(x)) = x$. Let's compute these one by one.

1. Check $f(g(x))$:

   • First, substitute $g(x)$ into $f(x)$: $f(g(x)) = \frac{2 \cdot \frac{10}{2x - 1} + 1}{10}$ Simplify this expression step by step.

2. Check $g(f(x))$:

   • Next, substitute $f(x)$ into $g(x)$: $g(f(x)) = \frac{10}{2 \cdot \frac{2x+1}{10} - 1}$ Simplify this to see if the result is $x$.

I'll now compute both expressions to verify whether the functions are inverses.The computations yield the following results:

1. $f(g(x)) = \frac{2x + 19}{10(2x - 1)}$
2. $g(f(x)) = \frac{25}{x - 2}$

Since neither $f(g(x))$ simplifies to $x$ nor $g(f(x))$ simplifies to $x$, the functions $f(x) = \frac{2x+1}{10}$ and $g(x) = \frac{10}{2x-1}$ are not inverses of each other.

Therefore, the correct answer is False.

Would you like more details on any part of the process? Here are some follow-up questions for further practice:

1. What does it mean for two functions to be inverses in general?
2. How can you algebraically derive the inverse of a given function?
3. Why is verifying $f(g(x)) = x$ and $g(f(x)) = x$ necessary to confirm that functions are inverses?
4. Can a function always have an inverse?
5. What would the graph of two inverse functions look like?

Tip: When finding the inverse of a function, remember to swap $x$ and $y$ and solve for $y$.