Computing (f+g) and (f·g)

Pre-Calculus · Axiom Academy

EXAMPLE Computing (f+g) and (f·g) Combine two functions by adding and multiplying their formulas, then evaluate at a point. Given the functions f(x) = x^2 + 3 and g(x) = 2x - 1 , find: Nice work — you built both combined functions from scratch and evaluated each one at a point. (f + g)(x): add the formulas, then combine like terms: (f + g)(x) = x^2 + 2x + 2 . (f · g)(x): multiply the formulas, then expand and simplify: . Evaluating: substitute the point into the combined formula — (f + g)(2) = 10 and . Shortcut check: since f(2) = 7 and g(2) = 3 , you also get 7 + 3 = 10 and — combining first or evaluating first gives the same result.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.