An equation that defines y as a function of x is given. (b) Find ƒ(3). y+2x^2=3-x

Key Concepts

Functions

A function is a relation that assigns exactly one output (y) for each input (x). In this context, the equation y + 2x² = 3 - x defines y as a function of x, meaning for every value of x, there is a corresponding value of y. Understanding functions is crucial for evaluating specific inputs, such as ƒ(3).

Solving Equations

Solving equations involves manipulating the equation to isolate the variable of interest. In this case, we need to rearrange the equation y + 2x² = 3 - x to express y in terms of x. This process is essential for finding the value of the function at a specific point, such as when x equals 3.

Substitution

Substitution is the process of replacing a variable in an expression or equation with a specific value. To find ƒ(3), we substitute x with 3 in the rearranged equation. This step is vital for calculating the output of the function at that particular input.