question_answer 31)

Let f, g and h be function from R to R. show that (f + g) oh = foh + goh (f.g)oh = (foh).(goh)  

Answer:

Let  be any element             = f(h(x)+ g(h(x))       = (foh) (x) + (goh) (x)       = (foh + goh) (x)       = (foh + goh) (x)             Also, ((f.g) oh) (x) = (f.g) (h(x))             = f(h(x)).g(h(x))             = (foh)(x). (goh)(x)             = ((foh).(goh) (x)             which is proved.