Evaluating Functions Evaluate the function at the indicated...

Evaluating Functions Evaluate the function at the indicated values.
$$
\begin{array}{l}{g(x)=\frac{1-x}{1+x}} \\ {g(2), g(-1), g\left(\frac{1}{2}\right), g(a), g(a-1), g\left(x^{2}-1\right)}\end{array}
$$

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Key Concepts

Algebraic Simplification

After substitution, algebraic simplification involves manipulating the resulting expression into its simplest form. This includes operations like combining like terms, reducing fractions, and canceling common factors.

Function Evaluation

This concept involves determining the output of a function by substituting specific values into the function's variable. In essence, it is about evaluating what the function produces when you change its input.

Substitution

Substitution is the process of replacing the variable in an expression or equation with a specific value or another expression. This directly applies to evaluating a function for particular inputs.

Domain Considerations

Domain considerations ensure that the function is properly defined for the given input values. This means checking that no operations, such as division by zero or negative square roots (in real numbers), occur when substituting the specific value.