Answer:
[tex]R=(0,inf)[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{3}{4|x|-3}[/tex]
The graph that belongs to this function is attached.
In the graph, you are able to see that all y-values of the given function are more than zero, that means the range of the function is any real number that is major than zero, that is
[tex]R=(0,inf)[/tex]
Another way to find this range, it's by isolating the x-variable:
[tex]y=\frac{3}{4|x|-3}[/tex]
[tex]y(4|x|-3)=3\\4|x|-3=\frac{3}{y} \\4|x|=\frac{3}{y}+3\\x=\frac{1}{4}( \frac{3}{y}+3)[/tex]
By isolating the x-variable, you can observe that the y-variable is at a position where it cannot be equal to zero, because when that happens the function is undetermined.
Therefore, the range for this function is
[tex]R=(0,inf)[/tex]
