Given, f: R → R and g: R → R
So, gof: R → R and fog: R → R
\[f\left( x \right)\text{ }=~{{x}^{2}}~+\text{ }2x~-\text{ }3\] and \[g\left( x \right)\text{ }=\text{ }3x~-\text{ }4\]
(gof) (x) = g (f(x))
\[=~g~({{x}^{2~}}+\text{ }2x\text{ }-\text{ }3)\]
\[=~3~({{x}^{2~}}+\text{ }2x\text{ }-\text{ }3)~-\text{ }4\]
\[=~3{{x}^{2~}}+~6x~-~9~-~4\]
\[=~3{{x}^{2~}}+\text{ }6x\text{ }-\text{ }13\]
Now, (fog) (x) = f (g (x))
\[=~f~\left( 3x\text{ }-\text{ }4 \right)\]
\[=~{{\left( 3x~-~4 \right)}^{2~}}+\text{ }2~\left( 3x~-~4 \right)~-3\]
\[=~9{{x}^{2~}}+\text{ }16\text{ }-\text{ }24x\text{ }+\text{ }6x\text{ }\text{ }8\text{ }-\text{ }3\]
\[=~9{{x}^{2~}}-\text{ }18x~+~5\]