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We are given two functions, \( f \) and \( g \), as sets of ordered pairs. The goal is to compute the value of \( T \) using the expression provided:

\[
T = \frac{f(g(1)) \times g(5) + f(2)}{g(f(3)) + g(4)}
\]

### Step 1: Identify the values from the given functions.

#### Function \( f \):
- \( f(3) = 5 \)
- \( f(2) = 1 \)
- \( f(5) = 4 \)

#### Function \( g \):
- \( g(1) = 2 \)
- \( g(4) = 5 \)
- \( g(5) = 3 \)

### Step 2: Substitute these values into the expression for \( T \).

First, evaluate each component step by step:

1. \( f(g(1)) = f(2) = 1 \)
2. \( g(5) = 3 \)
3. \( f(2) = 1 \)
4. \( g(f(3)) = g(5) = 3 \)
5. \( g(4) = 5 \)

Now substitute these values into the formula for \( T \):

\[
T = \frac{1 \times 3 + 1}{3 + 5} = \frac{3 + 1}{8} = \frac{4}{8} = \frac{1}{2}
\]

### Final Answer:
The value of \( T \) is \( \frac{1}{2} \).

Would you like more details, or do you have any questions?

Here are 5 related questions you could explore:
1. What is the definition of a function and how does it apply to ordered pairs?
2. How can you generalize this process for larger sets of functions?
3. What are the differences between injective, surjective, and bijective functions?
4. How would this calculation change if one of the ordered pairs were different?
5. Can we represent these functions graphically and interpret the result visually?

**Tip:** Always double-check the function values before substitution to avoid mistakes in evaluations.

Dadas las funciones f = {(3;5), (2;1), (5;4)} y g = {(1;2), (4;5), (5;3)}, determina el valor de T = (f(g(1)) * g(5) + f(2)) / (g(f(3)) + g(4))

Learn how to evaluate the expression T using two functions f and g defined as sets of ordered pairs. Follow step-by-step calculations to solve for T in this basic algebra problem, perfect for students in Grades 9-10.

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