Question

Which of the following are true for all functions f(x) and g(x)?

Select all that apply

(f + g)(x) = (g + f)(x)

(f – g)(x) = (g – f)(x)

(fg)(x) = (gf)(x)

(f ° g)(x) = (g ° f)(x)

Answer 1

True for all f, g:
- (f + g)(x) = (g + f)(x) — addition is commutative (f(x)+g(x)=g(x)+f(x)).
- (fg)(x) = (gf)(x) — pointwise multiplication is commutative (f(x)g(x)=g(x)f(x)).

False in general:
- (f – g)(x) = (g – f)(x) (usually not; they're negatives of each other unless f=g).
- (f ° g)(x) = (g ° f)(x) (composition is not generally commutative; e.g. f(x)=x+1, g(x)=2x gives f(g)(x)=2x+1 ≠ g(f)(x)=2x+2).