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G(x) = f(rx) f(x) = -3x + 5 g(x) = -1x + 5 Find r

G(x) = f(rx) f(x) = -3x + 5 g(x) = -1x + 5 Find r
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8 votes
G(x) = f(rx)
f(x) = -3x + 5
g(x) = -1x + 5

Find r

User Andrey Prokopiev
by
7.6k points

1 Answer

4 votes


\begin{cases} f(x)=-3x+5\\[1em] f(rx)=-3(rx)+5 \end{cases}\qquad \qquad \begin{cases} g(x)=-1x+5\\[1em] g(x)=f(rx)\\ \qquad -3(rx)+5 \end{cases} \\\\\\ \stackrel{g(x)}{-1x+5}~~=~~\stackrel{g(x)}{-3(rx)+5}\implies -x+5=-3rx+5\implies -x=-3rx \\\\\\ \cfrac{-x}{-x}=3r\implies 1=3r\implies \boxed{\cfrac{1}{3}=r}

User Ian Thompson
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8.7k points
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