Chapter 14.1, Problem 3WE

To determine

To find: The value of $f\left(3\right)$and $f\left(-3\right)$and check whether $f$ is a one-to-one function.

Answer to Problem 3WE

The value of $f\left(3\right)$ and $f\left(-3\right)$ is $10$ and the function $f$ is not a one to one function.

Explanation of Solution

Calculation:

Consider the given function $f\left(x\right)=x^2+1$ .

Substitute 3 for $x$ in the function.

  $\begin{array}{c}f\left(3\right)=3^2+1\\ =10\end{array}$

Substitute $-3$ for $x$ in the function.

  $\begin{array}{c}f\left(-3\right)={\left(-3\right)}^2+1\\ =10\end{array}$

So, the value of $f\left(3\right)$ and $f\left(-3\right)$ is $10$ .

From the above, it is clear that the function $f$ has same image value for $f\left(3\right)$ and $f\left(-3\right)$ . Therefore, the function $f$ is not a one-to-one.