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

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The domain of a function f(x) is all the values of x for which f(x) is real.

f(x) = sqrt ( 5 -|3x - 4|)

As sqrt is real for 0 or positive numbers

5 - |3x - 4| >=0

=> |3x - 4| <=5

This gives 3x - 4 <=5

=> x <=9/3

=> x <= 3

and 3x - 4 >=-5

=> 3x >= -1

=> x >= -1/3

**The domain is all values of x that lie in [-1/3 , 3]**

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]**