anyone know how to do: if f(x+3)=5-3x, find f(x)
starryblue Member Joined Apr 19, 2011 Messages 256 Location Australia Gender Female HSC 2013 Jul 28, 2011 #1 anyone know how to do: if f(x+3)=5-3x, find f(x)
xV1P3R Member Joined Jan 1, 2007 Messages 199 Gender Male HSC 2010 Jul 28, 2011 #2 Replace x with x - 3, and the following justifies it. g(x) = f(x+3) = 5 - 3x g(x-3) = f(x) = 5 - 3(x-3) = 5 - 3x + 9 = 14 - 3x
Replace x with x - 3, and the following justifies it. g(x) = f(x+3) = 5 - 3x g(x-3) = f(x) = 5 - 3(x-3) = 5 - 3x + 9 = 14 - 3x
Trebla Administrator Administrator Joined Feb 16, 2005 Messages 8,401 Gender Male HSC 2006 Jul 28, 2011 #3 Let u = x + 3 f(u) = 5 - 3(u - 3) = 14 - 3u Hence f(x) = 14 - 3x Alternatively, f(x + 3) = 5 - 3x => f(x + 3) = 5 - 3(x + 3 - 3) => f(x + 3) = 14 - 3(x + 3) Hence f(x) = 14 - 3x
Let u = x + 3 f(u) = 5 - 3(u - 3) = 14 - 3u Hence f(x) = 14 - 3x Alternatively, f(x + 3) = 5 - 3x => f(x + 3) = 5 - 3(x + 3 - 3) => f(x + 3) = 14 - 3(x + 3) Hence f(x) = 14 - 3x
