Question

The answers to 13 and 20 and how there done.

Answer 1

The sum and product of two functions $f(x)$ and $g(x)$, i.e. $(f+g)(x)$ and $(f\cdot g)(x)$ respectively, are simply defined as the sum and product of the expressions that define each function.

So, as for exercise 13, we have

$(f\cdot g)(x) = f(x)\cdot g(x) = (2x^3-5x^2)(2x-1) = 4 x^4- 12 x^3 +5 x^2$

Similarly, as for exercise 20, we have

$(g + f)(t) = g(t) + f(f) = (2t+5) + (-t^2+5) = -t^2 + 2t + 10$