Question

3-16 A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

14. \(f\left( x \right) = {x^{\bf{4}}} - \;{\bf{1}}\)

Short answer

The function is not one-to-one.

Step-by-step solution

Recall the definition of a one-to-one function

For a one-to-one function, the value of the functionshould not be the same in its domain.

Check for the given function

For the function \(f\left( x \right) = {x^4} - 16\), the values are \(f\left( 1 \right)\), and \(f\left( { - 1} \right)\) as shown below:

\(\begin{aligned}f\left( 1 \right) &= {1^4} - 1\\ &= 0\end{aligned}\)

And,

\(\begin{aligned}f\left( { - 1} \right) &= {\left( { - 1} \right)^4} - 1\\ &= 0\end{aligned}\)

Here, all the function has two similar values.

So, the given function is not a one-to-one function.