Key Concepts:
- Function substitution is performed by replacing variables in expressions with given function definitions.
- Operations with functions are performed by applying the operations to their expressions.
Skills Covered:
- Replacing variables in a given function with another function expression.
- Evaluating and simplifying function-based expressions.
Example Problems:
- If (f(x) = x^2 + 3x) and (g(x) = x - 2), find (f(g(x))); Solution: ((x-2)^2 + 3(x-2)) → Expand and simplify.
- If (f(x) = 2x) and (g(x) = x+1), find (f(x) \cdot g(x)); Solution: (2x \cdot (x+1) = 2x^2 + 2x).