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Substitution is a straightforward yet vital technique in mathematics. To substitute a value in a function means to replace the variable (usually represented by x) with a specific number. For example, in the given exercise, we are asked to find the value of the function when x is equal to 1. The function provided is:
**f(x) = 2x^2 - 5x + 3**
When we substitute x = 1 into the function, we replace every instance of x with 1:
**f(1) = 2(1)^2 - 5(1) + 3**
This is the preliminary step required to solve or evaluate functions and it is essential to perform it accurately.

Polynomial functions are expressions that involve variables raised to whole number exponents along with coefficients. The given function is a polynomial of the second degree (quadratic) because the highest exponent is 2. Let's break down the function:
**f(x) = 2x^2 - 5x + 3**
Here, 2 is the coefficient of the term with the highest power (x^2), -5 is the coefficient of x, and 3 is the constant term. Polynomial functions can have different degrees (1st degree for linear, 2nd degree for quadratic, and so on). They are essential in various fields of study, including physics, engineering, economics, and more. Understanding polynomials helps in graphing equations and solving real-world problems.

Simplifying expressions is the process of performing arithmetic operations to reduce a mathematical expression to its simplest form. After substituting the value of x, the next step is to simplify the expression. In our example:
**f(1) = 2(1)^2 - 5(1) + 3**
First, calculate the exponent: (1)^2 = 1. This makes the expression look like:
**2(1) - 5(1) + 3**
Next, perform the multiplication: 2 * 1 = 2 and -5 * 1 = -5. This changes our expression to:
**2 - 5 + 3**
Finally, combine the terms by performing the addition and subtraction from left to right: 2 - 5 = -3 and -3 + 3 = 0. So, we find that:** f(1)=0**
Understanding how to simplify expressions is critical for solving equations and making complex problems more manageable.