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Algebraic functions are expressions that involve variables and arithmetic operations such as addition, subtraction, multiplication, and division. These functions form the backbone of algebra and are employed to describe mathematical relationships in various fields.
In the given exercise, we encounter algebraic functions such as \( f(x) = 2x - 3 \) and \( g(t) = 5 + t \). Here, each function defines a rule that relates an input value to an output. For example, \( f(x) = 2x - 3 \) takes any real number \( x \), doubles it, and then subtracts 3 from the result.
Algebraic functions can be linear, as seen in \( f(x) = 2x - 3 \) and \( g(t) = 5 + t \), or they can be polynomial functions, such as \( G(x) = x^{2} + 2x - 7 \). Recognizing these forms allows us to understand how the function will behave and how to manipulate it effectively.

Substitution is a fundamental technique in algebra that involves replacing a variable with a specific number or expression. It is crucial when evaluating algebraic functions at specific points.
The exercise shows how substitution works in practice. For instance, evaluating \( f(-2) \) from \( f(x)=2x-3 \) means substituting \( -2 \) for \( x \) in the function. This transforms the expression into a numerical calculation: \( f(-2) = 2(-2) - 3 \).
Through substitution, we simplify expressions and evaluate specific values. This process turns a general function into a concrete number that we can work with or interpret further. It also provides insight into the behavior of functions at particular points.

Arithmetic operations are the basic operations of addition, subtraction, multiplication, and division used in mathematics. These operations are not only essential for managing numbers but also for manipulating algebraic expressions.
In the problem, arithmetic operations are used repeatedly to evaluate the functions and then to combine their results. After evaluating \( f(-2) = -7 \) and \( g(1) = 6 \), we perform the addition \( f(-2) + g(1) = -7 + 6 \). These operations allow us to condense and solve the expression to find a single numerical answer: \(-1\).
Mastering arithmetic operations ensures that you can solve various mathematical problems accurately, whether dealing with simple numbers or complex expressions. They are the building blocks of handling more advanced mathematical concepts.