6. Let FunliRR} be the vector space of all functions from R to R, with operations dened as follows: (i) For g E FunRJR}, f +9 is the function dened

Need help with the question,

The question is shown below.

6. Let FunliRflR} be the vector space of all functions from R to R, with operations defined as follows: (i) For fig E FunflRJR}, f +9 is the function defined by the rule (f+g)[:i:} := f[z)+g{z}.(ii) For f E FIm{]R,]R} and c E R, cf is the function defined by the rule (cfflz) := effic). Show that continuous functions form a. subspace of Fun(R,R). How about differentiablefunctions? Functions with the property f e f = f?