Understand the Properties of Functions

[mvola]

Homework Statement

Given f(x) = 1-x
Show that 2f(3x + 1) = -6x

Homework Equations

The Attempt at a Solution

I've tried many approaches, but I seem to be missing something. The latest approach was as follows and did not work.

Divide by 2.
f(3x + 1) = -3x
f(3x) + f(1) = -3x
3f(x) + f(1) = -3x
3(1-x) + 0 = -3x
3 - 3x = -3x
3 = 0 which is obviously not true.

Can anyone help me out with this?

 

[Dick]

Homework Statement

Given f(x) = 1-x
Show that 2f(3x + 1) = -6x

Homework Equations

The Attempt at a Solution

I've tried many approaches, but I seem to be missing something. The latest approach was as follows and did not work.

Divide by 2.
f(3x + 1) = -3x
f(3x) + f(1) = -3x
3f(x) + f(1) = -3x
3(1-x) + 0 = -3x
3 - 3x = -3x
3 = 0 which is obviously not true.

Can anyone help me out with this?

You are going about this completely the wrong way and using properties of f that aren't even true. To find f(3x+1) just substitute (3x+1) for x in 1-x. Doesn't that make more sense?

 

[Mandelbroth]

Homework Statement

Given f(x) = 1-x
Show that 2f(3x + 1) = -6x

$2f(3x+1)=2(1-(3x+1))=2(-3x)=-6x$.

Think of it this way: If $f(x)=1-x$, then $f(Lemon \, cake) = 1 - (Lemon \, cake)$, in the unlikely event that the quantity 1-(Lemon cake) is defined.

 

[mvola]

I was over-thinking it. Thank you!