Menu Close

fog-x-4x-1-g-x-x-2-f-x-




Question Number 192049 by sciencestudentW last updated on 06/May/23
fog(x)=4x−1  g(x)=x−2  f(x)=?
$${fog}\left({x}\right)=\mathrm{4}{x}−\mathrm{1} \\ $$$${g}\left({x}\right)={x}−\mathrm{2} \\ $$$${f}\left({x}\right)=? \\ $$
Answered by AST last updated on 06/May/23
f(g(x))=4x−1⇒f(x−2)=4(x−2)+7  ⇒f(x)=4x+7
$${f}\left({g}\left({x}\right)\right)=\mathrm{4}{x}−\mathrm{1}\Rightarrow{f}\left({x}−\mathrm{2}\right)=\mathrm{4}\left({x}−\mathrm{2}\right)+\mathrm{7} \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{4}{x}+\mathrm{7} \\ $$
Answered by qaz last updated on 07/May/23
f○g=f○ ((x),((x−2)) )= ((x),((4x−1)) )  ⇒f= ((x),((4x−1)) ) ((x),((x−2)) )^(−1) = ((x),((4x−1)) ) (((x−2)),(x) )= (((x−2)),((4x−1)) )= ((x),((4x+7)) )  ⇒f(x)=4x+7
$${f}\circ{g}={f}\circ\begin{pmatrix}{{x}}\\{{x}−\mathrm{2}}\end{pmatrix}=\begin{pmatrix}{{x}}\\{\mathrm{4}{x}−\mathrm{1}}\end{pmatrix} \\ $$$$\Rightarrow{f}=\begin{pmatrix}{{x}}\\{\mathrm{4}{x}−\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{x}−\mathrm{2}}\end{pmatrix}^{−\mathrm{1}} =\begin{pmatrix}{{x}}\\{\mathrm{4}{x}−\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}−\mathrm{2}}\\{{x}}\end{pmatrix}=\begin{pmatrix}{{x}−\mathrm{2}}\\{\mathrm{4}{x}−\mathrm{1}}\end{pmatrix}=\begin{pmatrix}{{x}}\\{\mathrm{4}{x}+\mathrm{7}}\end{pmatrix} \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{4}{x}+\mathrm{7} \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *