Answer to Question #262275 in Algebra for Carl

Question

the domain and range of f(x)= 2x+1/x-1

Answer 1

Solution;

$f(x)=\frac{2x+1}{x-1}$

Domain;

Means $x-1\neq0$ hence,$x\neq1$

The domain of f(x) is all real values expect -1.

Range;

Let $f(x)=\frac{2x+1}{x-1}=y$

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

$2x+1=yx-y$

$2x-yx=-1-y$

$x(2-y)=-1-y$

$x=\frac{-1-y}{2-y}$

Means that the quantity $2-y\neq0$

Hence;

$y\neq2$

The range of f(x) is all real values except 2.