Let \( f(x)=4 x+1 \) and \( g(x)=-2 x \). \( f(x)-g(x) \)

To find \( f(x) - g(x) \), we first need to substitute the given functions into the expression. Starting with \( f(x) = 4x + 1 \) and \( g(x) = -2x \), we calculate: \[ f(x) - g(x) = (4x + 1) - (-2x) = 4x + 1 + 2x = 6x + 1. \] So, the final expression for \( f(x) - g(x) \) is \( 6x + 1 \). If you want to explore the properties of this new function, \( f(x) - g(x) = 6x + 1 \) is a linear function with a slope of 6, indicating it rises steeply as \( x \) increases. You can quickly graph it to visualize how it behaves across different values of \( x \). For a real-world application, linear equations like this can represent many scenarios – such as calculating total costs where \( x \) could represent the number of items bought, and the equation will let you estimate your total spend quickly!