Chapter 10.1, Problem 46E

To determine

To check: The given statement is true or false.

Answer to Problem 46E

The statement is true.

Explanation of Solution

Given information:

The parametrically by $x=t$

And

  $y=f(t)$ for $-\infty <t<\infty$ .

Calculation:

Know that $f$ is a function with domain all real numbers then $y=f(x)$ where $-\infty <x<\infty$ .

Hence, for the parametrization

  $\begin{array}{c}x=t,\\ y=f(t),\\ -\infty <t<\infty \end{array}$

Of the curve

  $y=f(x)$

where

  $-\infty <x<\infty$

Then,

  $(x,f(x))=(t,f(t))$

For

  $-\infty <x=t<\infty$

Therefore, the required given statement is true.