​ If f(x) = √x (x ≥ 0) and g(x) = x^2 – 1 are two real functions, then find fog and gof and check whether fog = gof. ​

Question

If f(x) = \(\sqrt{x}\) (x ≥ 0) and g(x) = x² – 1 are two real functions, then find fog and gof and check whether fog = gof.

Answer 1

Computation of gof : 

Computation of fog : 

We find that fog and gof have distinct domains. 

Also, their formulae are not same.

Hence, fog ≠ gof