If f is a function such that #f(3)=2,f(4)=4 and f(x+4)=f(x+3)f(x+2)# for all integer #n>=0# then the value of #f(6)=?#

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Answer 1 · 2018-07-25T13:15:23

#f(6)=32#

Given that

#f(x+4)=f(x+3)f(x+2)\ ........(1)#

Setting #x=1# in above equation (1), we get

#f(1+4)=f(1+3)f(1+2)#

#f(5)=f(4)f(3)#

#f(5)=4\cdot 2\quad (\because \f(4)=4, \ f(3)=2 )#

#f(5)=8#

Setting #x=2# in above equation (1), we get

#f(2+4)=f(2+3)f(2+2)#

#f(6)=f(5)f(4)#

#f(6)=8\cdot 4\quad (\because \f(5)=8, \ f(4)=4 )#

#f(6)=32#