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If-f-x-1-2x-2-Find-f-x-




Question Number 205273 by hardmath last updated on 14/Mar/24
If   f(x−1)=2x+2  Find   f(x)=?
$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{2x}+\mathrm{2} \\ $$$$\mathrm{Find}\:\:\:\mathrm{f}\left(\mathrm{x}\right)=? \\ $$
Answered by Rasheed.Sindhi last updated on 14/Mar/24
Replace x by x+1     f(x)=2(x+1)+2=2x+4
$${Replace}\:\mathrm{x}\:{by}\:\mathrm{x}+\mathrm{1} \\ $$$$\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{2}=\mathrm{2x}+\mathrm{4} \\ $$
Answered by Rasheed.Sindhi last updated on 14/Mar/24
f(x−1)=2x−2+4                  =2(x−1)+4  Replace x−1 by x:  f(x)=2x+4
$${f}\left({x}−\mathrm{1}\right)=\mathrm{2}{x}−\mathrm{2}+\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}\left({x}−\mathrm{1}\right)+\mathrm{4} \\ $$$${Replace}\:{x}−\mathrm{1}\:{by}\:{x}: \\ $$$${f}\left({x}\right)=\mathrm{2}{x}+\mathrm{4} \\ $$
Answered by Skabetix last updated on 14/Mar/24
f(x−1+1)=f(x)=2(x+1)+2=2x+2+2=2x+4
$${f}\left({x}−\mathrm{1}+\mathrm{1}\right)={f}\left({x}\right)=\mathrm{2}\left({x}+\mathrm{1}\right)+\mathrm{2}=\mathrm{2}{x}+\mathrm{2}+\mathrm{2}=\mathrm{2}{x}+\mathrm{4} \\ $$

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