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.