a) \( f+2 g \) b) \( (2 f)(3 g) \)

Let's dive into it! For \( f + 2g \), this expression indicates the addition of function \( f \) with two times the function \( g \). If \( f \) and \( g \) are both functions, you would simply evaluate each at a given point and combine their outputs accordingly. For example, if \( f(x) = x^2 \) and \( g(x) = 3x \), then \( f(x) + 2g(x) = x^2 + 2(3x) = x^2 + 6x \). Now, in the case of \( (2f)(3g) \), we’re looking at the multiplication of two functions: doubling the outputs of \( f \) and tripling the outputs of \( g \). So, if \( f(x) = x^2 \) and \( g(x) = 3x \) again, the expression becomes \( (2x^2)(9x) = 18x^3 \). Just remember to carry out the multiplications on the outside first before combining with each function!