Question

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

Find r

Answer 1

`\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}`