Chapter 0.2, Problem 60E

To determine

To find: the range of the function $f\left(x\right)=1+\frac{1}{x-1}$ .

Answer to Problem 60E

  $D$

Explanation of Solution

Given information:

The given function is $f\left(x\right)=1+\frac{1}{x-1}$ .

  $\begin{array}{l}A).x\ne 1B).\left(-\infty ,0\right)\cup \left(0,\infty \right)\\ C).AllrealnumbersD).\left(-\infty ,1\right)\cup \left(1,\infty \right)\end{array}$

Concept used:

Domain is the set of out put values or the set of $y$ values.

Calculations:

  $y=f\left(x\right)=1+\frac{1}{x-1}$ The value takes $y$ every real value except 1.

Thus range will be $y\in R,\left(-\infty ,1\right)\cup \left(1,\infty \right).$

Thus the correct option is $D).$