Question

What is the range of the function f(x)=3/4|x|-3

Answer 1

the range of the answer is [-3,infinity) and {yly>=-3} 

Answer 2

`R=(0,inf)`

Explanation:

The given function is

`f(x)=(3)/(4|x|-3)`

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

`R=(0,inf)`

Another way to find this range, it's by isolating the x-variable:

`y=(3)/(4|x|-3)`

`y(4|x|-3)=3\\4|x|-3=(3)/(y) \\4|x|=(3)/(y)+3\\x=(1)/(4)( (3)/(y)+3)`

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

`R=(0,inf)`