Given f(x) = 2x, g(x) = x + 4, and h(x) = 5 – x3,
find (f + g)(2), (h – g)(2), (f × h)(2), and (h / g)(2).
To find the answers, I can either work symbolically (like in the previous example) and then evaluate, or I can find the values of the functions at x = 2 and then work from there. It's probably simpler in this case to evaluate first, so:
f(2) = 2(2) = 4
g(2) = (2) + 4 = 6
h(2) = 5 – (2)3 = 5 – 8 = –3
Now I can evaluate the listed expressions:
(f + g)(2) = f(2) + g(2) = 4 + 6 = 10
(h – g)(2) = h(2) – g(2) = –3 – 6 = –9
(f × h)(2) = f(2) × h(2) = (4)(–3) = –12
(h / g)(2) = h(2) ÷ g(2) = –3 ÷ 6 = –0.5
If you work symbolically first, and plug in the x-value only at the end, you'll still get the same results. Either way will work. Evaluating first is usually easier, but the choice is up to you.
