![\[x+1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c35c15a07d40573f958e4a5713f62604_l3.png "Rendered by QuickLaTeX.com")
![\[{{\mathbf{e}}^{\mathbf{x}}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-85ad8c0231e8868de5287e9b19e87cc3_l3.png "Rendered by QuickLaTeX.com")
Given f (x) =
![\[x\text{ }+\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-627fa7920249360b8e88bc0ce8f65e5f_l3.png "Rendered by QuickLaTeX.com")
, g(x) =
![\[{{e}^{x}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9cd4353dc9410ad9ea2e784965716187_l3.png "Rendered by QuickLaTeX.com")
![\[f:~R\to R~;~g:~R~\to ~[~1,~\infty )\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a145c7adfa40015550fcef9819f432c3_l3.png "Rendered by QuickLaTeX.com")
Now we have calculate fog:
Clearly, range of g is a subset of domain of f.
⇒ fog: R→R
(fog) (x) = f (g (x))
=
![\[f~({{e}^{x}})\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2c496c294720780a942d590b9f8024f4_l3.png "Rendered by QuickLaTeX.com")
=
![\[{{e}^{x~}}+\text{ }1\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-459539f5ec0d36f03933a1caf8f6c5d5_l3.png "Rendered by QuickLaTeX.com")
Now we have to compute gof,
Clearly, range of f is a subset of 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")
=
![\[{{e}^{x+1}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-461c8f5d4b39090d3fc28ad4191cdefa_l3.png "Rendered by QuickLaTeX.com")