# Find $$gof$$ and $$fog$$, if (i) $$f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;|$$

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

Toolbox:
• Let f,g, be two functions, the composition of functions gof is defined by, $(gof)(x) =g(f(x))$
• Let f,g, be two functions, the composition of functions fog is defined by, $(fog)(x)=f(g(x))$
(i)
Let the function f and g be defined by

$f(x)=|x| \qquad g(x)=|5x-2|$

Then,$(gof) (x)=f(g(x))$

$=g(|x|)$

Therefore gof (x) $=|5|x|-2|$

We also see that, $(fog)(x)=f(g(x))$

$=f(|5x-2|)$

$=\bigg||5x-2|\bigg|$

since we know that for any y,$||y||=|y|$

therefore we see that fog(x) $= |5x-2|$

edited Mar 19, 2013