Find the domain of f(x) = sqrt (5-l 3x-4l).

Given that f(x) = sqrt( 5- l 3x-4l
)

We need to find the domain of
f(x).

Since the function is a square root, then the domain
is all x values such the function inside the square root is positive or
0.

==> 5 - l 3x -4 l >=
0

Let us subtract
5.

==> - l 3x-4l >=
-5

==> l 3x-4 l =<
5

Now by definition we will
rewrite.

==> -5 =< 3x-4 =<
5

Add 4 to all
sides.

==> -1 =< 3x =<
9

Divide by 3.

==> -1/3
=< x =< 3

Then the domain of
f(x) is x= [ -1/3, 3]