Given #f(x)# is a polynomial function of #x#, satisfying #f(x)*f(y)= f(x) +f(y)+f(x y)-2# and that #f(2)=5#. Then #f(3)# is equal to? A) 10 B) 24 C) 15 D) none

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Answer 1 · 2017-03-06T21:19:14

option #d)#

#f(1)f(3)=f(1)+f(3)+f(3)-2# then

#f(3)(f(1)-2)=f(1)-2->f(3) = (f(1)-2)/(f(1)-2)#

To avoid indeterminations

#f(1)cdot f(1) = f(1)+f(1)+f(1)-2# or

#f(1)^2-3f(1)+2=0#

solving for #f(1)# we have

#f(1)={1,2}# so taking #f(1)= 1# we have finally

#f(3) = 1#