Question:
Find $f o g(2)$ and $g o f(1)$ when : $f: R \rightarrow R ; f(x)=x^{2}+8$ and $g: R \rightarrow R ; g(x)=3 x^{3}+1$
Solution:
$(f o g)(2)=f(g(2))=f\left(3 \times 2^{3}+1\right)=f(25)=25^{2}+8=633$
$(g o f)(1)=g(f(1))=g\left(1^{2}+8\right)=g(9)=3 \times 9^{3}+1=2188$