Question

Let f(x) = x² + x + 1 and g(x) = sin x. Show that fog ≠ gof.

Answer 1

Given as f(x) = x² + x + 1 and g(x) = sin x

Let us prove fog ≠ gof

(fog)(x) = f(g(x)) 

= f(sin x) 

= sin² x + sin x + 1

And (gof)(x) = g(f(x)) 

= g(x² + x + 1) 

= sin(x²+ x + 1)

Therefore, fog ≠ gof.