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Algebra
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For each pair of functions f and g below, find f(g(x)) and g(f(x)).  Then, determine whether f and g are inverse of each other.

Simplify answers as much possible.  Assume that your expressions are defined for all x in the domain of the composition.
a)   f(x)= x-1/2,   g(x)=2x-1,    f(g(x))= ,   g(f(x))=
b)  f(x)=-3/x, x≠0,  g(x)=3/x,x≠0,  f(g(x)),  g(f(x))
Oct 31st, 2015

Hello!

a) f(g(x))=g(x)-1/2=2x-3/2,

g(f(x))=2f(x)-1=2x-2.

is not = x, so isn't inverse.

b) f(g(x))=-3/g(x)=-x,

g(f(x))=3/f(x)=-x.

Also is not=x, so isn't inverse.

Please ask if something is unclear.
Oct 31st, 2015

question was incorrect first was x-1

Oct 31st, 2015

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Oct 31st, 2015
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