Question

Consider a function $f:x\to \frac{x+a}{x-1}:x\in R-\left\{1\right\}$where $a$ is a real constant, If $f$ is not a constant function answer the following

Range of $f$

• A. $R$
• B. $R-\left\{1\right\}$
• C. $R-\left\{0\right\}$
• D. None of these

Answer 1

Answer: (B)

$R-\left\{1\right\}$

Here, $f\left(x\right)=\frac{x+a}{x-1}$

Substitute $f\left(x\right)=y$

$y=\frac{x+a}{x-1}$

$\Rightarrow xy-y=x+a$

$\Rightarrow x=\frac{a+y}{y-1}$

For $x$ to be defined,

$y\ne 1$

Hence, the range of $y$ is all real values except 1 i.e $R-\left\{1\right\}$