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Given f:R->R and g:R->R , we define the sum f+g by (f+g)(x)= f(x)+g(x) and the product fg by (fg)(x)=f(x)*g(x) for all xinR . Find counterexamples
Given
f:R->R
and
g:R->R
, we define the sum
f+g
by
(f+g)(x)=
f(x)+g(x)
and the product
fg
by
(fg)(x)=f(x)*g(x)
for all
xinR
. Find counterexamples for the following.\ (a) If
f
and
g
are bijective, then the sum
f+g
is bijective.\ (b) If
f
and
g
are bijective, then the product
fg
is bijective.
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