![\[\mathbf{2x}~+~\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4c517b842b83ba7529b9fbc07262bea7_l3.png "Rendered by QuickLaTeX.com")
Given f (x) =
![\[x+1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c35c15a07d40573f958e4a5713f62604_l3.png "Rendered by QuickLaTeX.com")
, g (x) =
![\[2x~+~3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-da1c221d6bedd96a602dacfb0191ad06_l3.png "Rendered by QuickLaTeX.com")
f: R→R ; g: R → R
Now we have to compute fog
Clearly, the range of g is a subset of the domain of f.
⇒ fog: R→ R
(fog) (x) = f (g (x))
=
![\[f~\left( 2x+3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-22df10da1edb6d3d7c96df9c861cf2d9_l3.png "Rendered by QuickLaTeX.com")
=
![\[2x~+~3~+~1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1830254ba85ddd4b238174c2ddaf6580_l3.png "Rendered by QuickLaTeX.com")
=
![\[2x~+~4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f16ab691db2818a37b26f6435436377_l3.png "Rendered by QuickLaTeX.com")
Now we have to compute gof
Clearly, the range of f is a subset of the domain of g.
⇒ fog: R → R
(gof) (x) = g (f (x))
=
![\[g~\left( x+1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-4e0b10f638b666bf649ba48441127c91_l3.png "Rendered by QuickLaTeX.com")
=
![\[2~\left( x~+~1 \right)~+~3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a2f9299cdbfed8ce30b84cae34ff46eb_l3.png "Rendered by QuickLaTeX.com")
=
![\[2x~+~5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-270dbb44fd0332bbad169766eb080584_l3.png "Rendered by QuickLaTeX.com")