Question

Find the range of the following function;
$y=\frac{1}{x+3}-5$

Answer 1

The range of the function is the same as the domain of the inverse function.

So, interchanging $x$ and $y$

$x=\frac{1}{y+3}-5$

Solving for $y$, we get,

$y=\frac{1}{x+5}-3$

The excluded value in the domain of the inverse function can be determined by equating the denominator to zero and solving for $x$.

$x+5=0$

$x=-5$

So, the domain of the inverse function is a set of real numbers except $-5$

That is, the range of the given function is the set of real numbers except $-5$

So, Range ={$y\in R,y\ne -5$}