![\[\left| x \right|\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0120e579cd10e2831e2af204e58c5309_l3.png "Rendered by QuickLaTeX.com")
Given
![\[f~\left( x \right)~=~\left| x \right|\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c4388a507037ae86970256abdacb8100_l3.png "Rendered by QuickLaTeX.com")
,g(x) = sin x
![\[f:~R~\to ~(0,~\infty )~;~g~:~R\to [-1,~1]\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7a743a78cca0e67dfbe83167431a4de4_l3.png "Rendered by QuickLaTeX.com")
Now we have to calculate fog,
Clearly, the range of g is a subset of the domain of f.
⇒ fog: R→R
(fog) (x) = f (g (x))
= f (sin x)
=
![\[\left| sin~x \right|\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-645d651abfee19a702c70a7d87ac49c1_l3.png "Rendered by QuickLaTeX.com")
Now we have to calculate gof,
Clearly, the range of f is a subset of the domain of g.
⇒ fog : R→ R
(gof) (x) = g (f (x))
=
![\[g~\left( |x| \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-372ebb57fef90288a0b54fc84f86018e_l3.png "Rendered by QuickLaTeX.com")
=
![\[sin~\left| x \right|\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-731b157d36857d3eb44e832add6498ce_l3.png "Rendered by QuickLaTeX.com")