Chapter 10, Problem 17CT

To determine

To restrict the domain.

Answer to Problem 17CT

  $[3,\infty )$

Explanation of Solution

Given information: $f\left(x\right)={\left(x-3\right)}^2$

Formula Used: Inverse Relation

Calculation:

If a function is not one-to-one, it cannot have an inverse. If restrict the domain of the function so that it becomes one-to-one, thus creating a new function, this new function will have an inverse.

Since quadratic functions are not one-to-one, so, restrict their domain in order to find their inverses.

  

The domain of the function $f\left(x\right)={\left(x-3\right)}^2$ is $(-\infty ,\infty )$

But in this interval the function is not one-to-one.

So, restrict their domain in order to find their inverse.

From the graph, the function $f\left(x\right)={\left(x-3\right)}^2$ is one-to-one function in the interval $[3,\infty )$

So, restrict their domain from $(-\infty ,\infty )$ to $[3,\infty )$ in order to find the inverse of the function.