How do you find the domain and range of $\frac{5 x + 3}{1 - 2 x}$ $(5x+3)/(1-2x)$ ?

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Answer 1 · 2016-06-22T19:54:12

The domain is $RR-(1/2)$ and the range is $RR-(-5/2)$

the domain is obtained by finding the values for x so that:

$1-2x!=0`$

or

$x!=1/2$

Then, in order to find the range, let's calculate the inverse function of $y=(5x+3)/(1-2x)$ :

You need some steps:

$y(1-2x)=5x+3$

$y-2xy=5x+3$

$5x+2xy=y-3$

$x(5+2y)=y-3$

$x=(y-3)/(5+2y)$

so the range is obtained by the values y:

$5+2y!=0$

or

$y!=-5/2$

How do you find the domain and range of (5x+3)/(1-2x)5x+31−2x(5x+3)/(1-2x)?