Will fo(g + h) = (fog) + (foh)

L e t f, g, a n d h b e t h e f u n c t i o n f r o m R t o R . S o, f \circ (g + h) (x) = f ((g + h) x) (B y D e f i n i t i o n o f c o m p o s i t e f u n c t i o n) = f (g (x) + h (x)) = f (g (x)) + f (h (x)) (B y D e f i n i t i o n o f s u m f u n c t i o n) = (f \circ g) x + (f \circ h) x (B y D e f i n i t i o n o f c o m p o s i t e f u n c t i o n) = (f \circ g + f \circ h) x (B y D e f i n i t i o n o f s u m f u n c t i o n) \Rightarrow f \circ (g + h) = f \circ g + f \circ h ((B y D e f i n i t i o n o f e q u a l f u n c t i o n))