Question

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

Answer 1

Answer:

$R=(0,inf)$

Step-by-step explanation:

The given function is

$f(x)=\frac{3}{4|x|-3}$

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:

$y=\frac{3}{4|x|-3}$

$y(4|x|-3)=3\\4|x|-3=\frac{3}{y} \\4|x|=\frac{3}{y}+3\\x=\frac{1}{4}( \frac{3}{y}+3)$

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

$R=(0,inf)$

Answer 2

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