The answer is clear with writing Let f g R rightarrow R be f

The answer is clear with writing

Let f, g: R rightarrow R be functions defined by f(x) = x^3 + x^2 and g(x) = 4x - 9. Find f g and g f. What can you conclude about the commutativity of the operation?

Solution

fog = (4x-9)^3 + (4x-9)^2

= 64x^3 - 729 -3*16x^2 * 9 + 3*4x*81 + 16x^2+81 - 72x

= 64x^3 -416x^2 + 900x - 648

gof= 4(x^3 + x^2 ) -9 = 4x^3 + 4x^2 - 9