91Ó°ÊÓ

To evaluate a function, you substitute the given input value into the function's equation.
For example, in the exercise, we need to evaluate two functions: \(f(x)=-2x+3\) and \(g(x)=x^2 -5\).
This means we will replace 'x' with a specific value to find the output.
When we evaluated \(g(x)\) at \(x=1\):
\[g(1) = 1^2 - 5 = 1 - 5 = -4\]
Similarly, when we evaluated \(f(x)\) at \(x=1\):
\[f(1) = -2(1) + 3 = -2 + 3 = 1\]
The simplest way to ensure you are correctly substituting and simplifying is to follow the function's rules carefully.
Remember that a function maps every input to exactly one output.
Evaluating functions properly sets the foundation for more complex operations.

Function operations include tasks such as addition, subtraction, multiplication, and division of functions.
In the exercise, we used subtraction to subtract one function's output from another.
Here, after evaluating \(g(1)\) and \(f(1)\), we found the difference:

Steps recap:
1. Evaluated \(g(1) = -4\)
2. Evaluated \(f(1) = 1\)
3. Subtracted: \[g(1) - f(1) = -4 - 1 = -5\]

Function operations allow us to combine and compare different functions to see how their outputs interact.
These operations can often reveal critical insights, especially in higher-level math.

An algebraic expression involves numbers, variables, and operations.
In this exercise, both given functions, \(f(x) = -2x + 3\) and \(g(x) = x^2 - 5\) are algebraic expressions.
They include coefficients (numbers in front of variables), constants (stand-alone numbers), and variables (like 'x').

Understanding algebraic expressions involves:
- Recognizing and applying different operations (addition, subtraction, etc.)
- Simplifying expressions by combining like terms (terms with the same variable and power)
- Substituting values into expressions to evaluate the output, as we did in the exercise.

This strong grasp of algebraic expressions helps in solving equations and understanding functions, as we see in this example.
Combining the basics of algebraic expressions, you create a solid platform for more advanced topics in mathematics.