Let ƒ(x)=-3x+4 and g(x)=-x^2+4x+1. Find each of the following. Simplify if necessary. See Example 6. ƒ(2m-3)

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. For example, if you have a function f(x) and you want to find f(a), you replace x with a in the function's expression. This process is essential for solving problems that require finding the value of a function at a given point.

Linear Functions

A linear function is a polynomial function of degree one, typically expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept. In the given function f(x) = -3x + 4, the slope is -3, indicating a decrease in value as x increases. Understanding linear functions is crucial for analyzing their behavior and graphing them.

Substitution in Functions

Substitution in functions refers to replacing a variable in a function with another expression or value. In this case, substituting 2m - 3 into f(x) means calculating f(2m - 3) by replacing x in the function's formula with the expression 2m - 3. This technique is fundamental in algebra for manipulating and simplifying expressions.