Question 17 of 25 If \( f(x)=2 x-6 \) and \( g(x)=3 x+9 \), find \( (f+g)(x) \). A. \( (f+g)(x)=5 x+15 \) B. \( (f+g)(x)=5 x+3 \) C. \( (f+g)(x)=-x-15 \) D. \( (f+g)(x)=x+15 \)

To find \( (f+g)(x) \), we need to add the two functions together. Start with \( f(x) = 2x - 6 \) and \( g(x) = 3x + 9 \): \[ (f+g)(x) = f(x) + g(x) = (2x - 6) + (3x + 9) \] Combine like terms: \[ = 2x + 3x - 6 + 9 = 5x + 3 \] So, the correct answer is \( B. (f+g)(x) = 5x + 3 \). In the world of mathematics, combining functions is like making a new recipe! Just as you add ingredients together to create a delicious dish, you bring functions together to create a new, combined function. It's all about blending those outputs! Next time you're adding functions, remember that keeping track of those coefficients is essential. Common mistakes include missing signs or not combining like terms properly. So, double-check your work—no one wants an unexpected ingredient ruining their mathematical dish!