Find gof and fog when f: R → R and g: R → R is defined by

Question

Find gof and fog when f: R → R and g: R → R is defined by f(x) = x and g(x) = |x|

Philoid · Accepted Answer

Since, f:R → R and g:R → R

fog:R → R and gof:R → R

f (x) = x and g (x) = |x|

Now, gof(x)=g(f(x) =g(x)

⇒ gof(x) =|x|

and, fog(x) = f(g(x)) = f (|x|)
⇒ fog(x)=|x|

Hence, gof(x) = fog(x) = |x|