Question

If $f\left(x\right)=x^2+1$, find $f\left(3\right)$ and $f\left(-3\right)$. Is $f$ a one-to-one function?

Short answer

The value of $f\left(3\right)$and $f\left(-3\right)$ is 10 and the function f isnot a one to one function.

Step-by-step solution

Step 1. Given Information.

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

Step 2. Calculation.

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 $f\left(-3\right)$.

Step 3. Conclusion.

Therefore, the function f is not a one-to-one.