Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 152671 by liberty last updated on 31/Aug/21

Commented by MJS_new last updated on 31/Aug/21

f(1)=5  f(2)=f(1+1)=f(1)+6×1+4=15  f(3)=f(2+1)=f(2)+6×2+4=31  but  f(3)=f(3×1)=4f(1)+1=21  something′s wrong

$${f}\left(\mathrm{1}\right)=\mathrm{5} \\ $$$${f}\left(\mathrm{2}\right)={f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{6}×\mathrm{1}+\mathrm{4}=\mathrm{15} \\ $$$${f}\left(\mathrm{3}\right)={f}\left(\mathrm{2}+\mathrm{1}\right)={f}\left(\mathrm{2}\right)+\mathrm{6}×\mathrm{2}+\mathrm{4}=\mathrm{31} \\ $$$$\mathrm{but} \\ $$$${f}\left(\mathrm{3}\right)={f}\left(\mathrm{3}×\mathrm{1}\right)=\mathrm{4}{f}\left(\mathrm{1}\right)+\mathrm{1}=\mathrm{21} \\ $$$$\mathrm{something}'\mathrm{s}\:\mathrm{wrong} \\ $$

Commented by liberty last updated on 31/Aug/21

from f(x+1)=f(x)+6x+4  x=1⇒f(2)=5+6+4=15  x=2⇒f(3)=15+12+4=31  x=3⇒f(4)=31+18+4=53  x=4⇒f(5)=53+24+4=91  x=5⇒f(6)=91+30+4=125  therefore fix the question   something wrong

$$\mathrm{from}\:\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{f}\left(\mathrm{x}\right)+\mathrm{6x}+\mathrm{4} \\ $$$$\mathrm{x}=\mathrm{1}\Rightarrow\mathrm{f}\left(\mathrm{2}\right)=\mathrm{5}+\mathrm{6}+\mathrm{4}=\mathrm{15} \\ $$$$\mathrm{x}=\mathrm{2}\Rightarrow\mathrm{f}\left(\mathrm{3}\right)=\mathrm{15}+\mathrm{12}+\mathrm{4}=\mathrm{31} \\ $$$$\mathrm{x}=\mathrm{3}\Rightarrow\mathrm{f}\left(\mathrm{4}\right)=\mathrm{31}+\mathrm{18}+\mathrm{4}=\mathrm{53} \\ $$$$\mathrm{x}=\mathrm{4}\Rightarrow\mathrm{f}\left(\mathrm{5}\right)=\mathrm{53}+\mathrm{24}+\mathrm{4}=\mathrm{91} \\ $$$$\mathrm{x}=\mathrm{5}\Rightarrow\mathrm{f}\left(\mathrm{6}\right)=\mathrm{91}+\mathrm{30}+\mathrm{4}=\mathrm{125} \\ $$$$\mathrm{therefore}\:\mathrm{fix}\:\mathrm{the}\:\mathrm{question}\: \\ $$$$\mathrm{something}\:\mathrm{wrong} \\ $$

Answered by Rasheed.Sindhi last updated on 31/Aug/21

f(1)=5;f(3x)=4f(x)+1_((1)) ;f(x+1)=f(x)+6x+4_((2)) ;f(x)=?  ^((2)⇒) f(1+1)=f(1)+6(1)+4=5+6+4=15  f(2)=15  ^((1)⇒) f(3×2)=4f(2)+1=4(15)+1=61  f(6)=61

$${f}\left(\mathrm{1}\right)=\mathrm{5};\underset{\left(\mathrm{1}\right)} {\underbrace{{f}\left(\mathrm{3}{x}\right)=\mathrm{4}{f}\left({x}\right)+\mathrm{1}}};\underset{\left(\mathrm{2}\right)} {\underbrace{{f}\left({x}+\mathrm{1}\right)={f}\left({x}\right)+\mathrm{6}{x}+\mathrm{4}}};{f}\left({x}\right)=? \\ $$$$\:^{\left(\mathrm{2}\right)\Rightarrow} {f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{6}\left(\mathrm{1}\right)+\mathrm{4}=\mathrm{5}+\mathrm{6}+\mathrm{4}=\mathrm{15} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{15} \\ $$$$\:^{\left(\mathrm{1}\right)\Rightarrow} {f}\left(\mathrm{3}×\mathrm{2}\right)=\mathrm{4}{f}\left(\mathrm{2}\right)+\mathrm{1}=\mathrm{4}\left(\mathrm{15}\right)+\mathrm{1}=\mathrm{61} \\ $$$${f}\left(\mathrm{6}\right)=\mathrm{61} \\ $$

Answered by chengulapetrom last updated on 31/Aug/21

f(3(1))=4f(1)+1  f(3)=21  f(1+1)=f(1)+6+4  f(2)=15  f(3×2)=4f(2)+1  f(6)=4×15+1  f(6)=61

$${f}\left(\mathrm{3}\left(\mathrm{1}\right)\right)=\mathrm{4}{f}\left(\mathrm{1}\right)+\mathrm{1} \\ $$$${f}\left(\mathrm{3}\right)=\mathrm{21} \\ $$$${f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{6}+\mathrm{4} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{15} \\ $$$${f}\left(\mathrm{3}×\mathrm{2}\right)=\mathrm{4}{f}\left(\mathrm{2}\right)+\mathrm{1} \\ $$$${f}\left(\mathrm{6}\right)=\mathrm{4}×\mathrm{15}+\mathrm{1} \\ $$$${f}\left(\mathrm{6}\right)=\mathrm{61} \\ $$

Answered by Olaf_Thorendsen last updated on 31/Aug/21

f(6) = f(3×2) = 4f(2)+1  = 4f(1+1)+1 = 4(f(1)+6×1+4)+1  = 4(5+10)+1 = 61

$${f}\left(\mathrm{6}\right)\:=\:{f}\left(\mathrm{3}×\mathrm{2}\right)\:=\:\mathrm{4}{f}\left(\mathrm{2}\right)+\mathrm{1} \\ $$$$=\:\mathrm{4}{f}\left(\mathrm{1}+\mathrm{1}\right)+\mathrm{1}\:=\:\mathrm{4}\left({f}\left(\mathrm{1}\right)+\mathrm{6}×\mathrm{1}+\mathrm{4}\right)+\mathrm{1} \\ $$$$=\:\mathrm{4}\left(\mathrm{5}+\mathrm{10}\right)+\mathrm{1}\:=\:\mathrm{61} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com