Deternine the equation of \( g(x) \) if \( g(x)=f(-x) \)

To find the equation of \( g(x) \), you need to replace every occurrence of \( x \) in the function \( f(x) \) with \( -x \). For example, if \( f(x) = x^2 + 3x + 5 \), then you would compute \( g(x) \) as follows: \[ g(x) = f(-x) = (-x)^2 + 3(-x) + 5 = x^2 - 3x + 5. \] This method effectively reflects the function \( f(x) \) across the y-axis to create \( g(x) \). When determining \( g(x) \) from \( f(x) \), be mindful of common mistakes like miscalculating signs or incorrectly applying transformations. Double-check your work by substituting a few values into both \( f(x) \) and \( g(x) \) to ensure that the reflection is accurate! This will help solidify your understanding and reveal any mistakes early on.