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Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
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Find \( gof\) and \(fog\), if \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)

Note: This is part 1st of a 2 part question, split as 2 separate questions here.

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  • Given two functions $f:A \to B $ and $g:B \to C$, then composition of $f$ and $g$, $gof:A \to C$ by $ gof (x)=g(f(x))\;for\; all \;x \in A$
  • Given two functions $g:A \to B $ and $f:B \to C$, then composition of $g$ and $g$, $fog:A \to C$ by $ fog (x)=f(g(x))\;for\; all \;x \in A$
Given $f(x)=|x|, \; g(x)=|5x-2|$
Step 1: Given two functions $f:A \to B $ and $g:B \to C$, then composition of $f$ and $g$, $gof:A \to C$ by $ gof (x)=g(f(x))\;for\; all \;x \in A$
Since $f(x) = |x|, \rightarrow gof = g(f(x)) = g(|x|) =|5|x|-2|$,
Step 2: Given two functions $g:A \to B $ and $f:B \to C$, then composition of $g$ and $g$, $fog:A \to C$ by $ fog (x)=f(g(x))\;for\; all \;x \in A$
Since $g(x) = |5x-2|, \rightarrow fog = f(g(x)) = f(|5x-2|) =||5x-2|| = |5x-2|$,
answered Mar 7, 2013 by meena.p
edited Mar 19, 2013 by balaji.thirumalai
 

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