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

Key Concepts

Function Evaluation

Function evaluation involves substituting a specific input value into a function to determine its output. In this case, we need to evaluate the function ƒ(x) at the input (3t - 2). This process requires replacing every instance of 'x' in the function's expression with the given input.

Linear Functions

A linear function is a polynomial function of degree one, which can be expressed in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. The function ƒ(x) = -3x + 4 is linear, indicating that its graph is a straight line. Understanding the properties of linear functions is essential for evaluating and simplifying expressions involving them.

Simplification of Expressions

Simplification involves reducing an expression to its simplest form, making it easier to understand or compute. After substituting (3t - 2) into the function ƒ(x), we will perform algebraic operations to simplify the resulting expression. This may include combining like terms and applying the distributive property.