What is the range of f(x) = 1-3x if the domain is x>0?

We'll have to determine the set of real numbers that
variable x can take, such as the expression that defines the function to be
real.

We'll set f(x) = y = 1 -
3x

We'll move the term in x to the left and the term in y
to the right:

3x = 1 - y

We'll
divide by 3:

x = (1-y)/3

We
know, from enunciation, that x>0, therefore (1-y)/3 >
0.

We'll solve the
inequality:

(1-y)/3 >
0

1 - y > 0

-y >
-1

We'll multiply by -1 and we'll change the direction of
inequality:

y <
1

Therefore, the range of the function f is
the opened interval (-`oo` ; 1).