Help with functions (1 Viewer)

[starryblue]

anyone know how to do: if f(x+3)=5-3x, find f(x)

 

[xV1P3R]

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]

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