Let f: R → R and g: R → R be defined by f(x) = x² and g(x) = x + 1. Show that fog ≠ gof.

Question

Let f: R → R and g: R → R be defined by f(x) = x 2 and g(x) = x + 1. Show that fog ≠ gof.

Philoid · Accepted Answer

We have, f: R → R and g: R → R are two functions defined by

f (x)= x² and g(x) = x + 1

Now,

fog (x) = f(g(x)) = f(x + 1) =(x + 1)²

⇒ fog(x) = x² + 2x + 1 ……(i)

gof(x) = g(f(x)) = g(x²) = x² + 1 ……(ii)

from (i) & (ii)

fog ≠ gof

Let f: R → R and g: R → R be defined by f(x) = x2 and g(x) = x + 1. Show that fog ≠ gof.