How do you find (g o f)(x) given #f(x)= x/(x-2)#, #g(x)=3/x#?

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Answer 1 · 2015-12-19T19:35:53

#(g@f)(x) = (3x-6)/x#

#(g @ f)(x) # just means that #g# is a function of #f(x)#, so we need to replace #x# in #g(x)# with #f(x)#.

#g(x) = 3/x#

Replace each #x# with #f(x)#. In this case, there is only one.

#(g@f)(x) = 3/f(x)#

Now plug in the value of #f(x)#.

#(g@f)(x) = 3/(x/(x-2))#

Simplify.

#(g@f)(x) = (3(x-2))/x#

#(g@f)(x) = (3x-6)/x#