When performing the composition of two functions f(x)𝑓(𝑥) and g(x)𝑔(𝑥), [f∘g](x)[𝑓∘𝑔](𝑥)    and    [g∘f](x)[𝑔∘𝑓](𝑥) will produce the same answer.Question 5Select one:TrueFalse

composition of functions?

Suppose that the functions f and g are defined as follows.=fx≠95x, x0=gx−7x9Find the compositions ∘ff and ∘gg.Simplify your answers as much as possible.(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.)=∘ffx=∘ggx

Composition of two functions is always commutative.Group startsTrue or FalseTrue, unselectedFalse, unselected

Suppose 𝐹(𝑥)=𝑥2𝑥2−7F(x)= x 2 −7x 2 ​ , and 𝐹(𝑥)=(ℎ∘𝑔)(𝑥)F(x)=(h∘g)(x). Which of the following are possible definitions for h and g?I. ℎ(𝑥)=𝑥,𝑔(𝑥)=𝑥2𝑥2−7II. ℎ(𝑥)=𝑥2,𝑔(𝑥)=𝑥𝑥−7III. ℎ(𝑥)=𝑥4𝑥4−7,𝑔(𝑥)=∣𝑥∣IV. ℎ(𝑥)=𝑥𝑥−7,𝑔(𝑥)=𝑥2​ I. h(x)=x,g(x)= x 2 −7x 2 ​ II. h(x)=x 2 ,g(x)= x−7x​ III. h(x)= x 4 −7x 4 ​ ,g(x)= ∣x∣​ IV. h(x)= x−7x​ ,g(x)=x 2 ​ A.II and III onlyB.I and II onlyC.I and IV onlyD.I, III and IV onlyE.I, II, III and IV

Suppose f(x) =1𝑥x1​ then (𝑓∘𝑓∘𝑓)(𝑥)(f∘f∘f)(x) =A.11𝑥x1​ 1​ B.1𝑥x1​ C.𝑥2x 2 D.1𝑥2x 2 1​ E.xSUBMITarrow_backPREVIOUS