Let f : R → R and g : R → R be defined by

Question:

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x)=x^{2}$ and $g(x)=x+1$. Show that fog $\neq g$ of.

Solution:

Given, $f: R \rightarrow R$ and $g: R \rightarrow R$.

So, the domains of $f$ and $g$ are the same.

$(f o g)(x)=f(g(x))=f(x+1)=(x+1)^{2}=x^{2}+1+2 x$

$(g o f)(x)=g(f(x))=g\left(x^{2}\right)=x^{2}+1$

So,  fog ≠ gof