Chapter 2.7, Problem 20E

To determine

To prove the function $f(x)=\frac{1}{x^{}}$ is one-to-one function

Answer to Problem 20E

  $x_1=x_2$

Yes it isaone-to-one function

Explanation of Solution

Given information:

  $f(x)=\frac{1}{x^{}}$

Calculation:

Put $x=x_1,x_2$

Therefore,

  $f(x_1)=\frac{1}{x_1}$

And

  $f(x_2)=\frac{1}{x_2}$

For one-to-one

  $f(x_1)=f(x_2)$

  $\frac{1}{x_1}=\frac{1}{x_2}$ [Cross multiply both the sides]

  $x_1=x_2$

Hence $x_1=x_2$

So it is a one-to-one function