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.

9. \(f\left( x \right) = {\bf{2}}x - {\bf{3}}\)

Short answer

The function is 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 function should not be the same in its domain.

Check for the given function

If \({x_1} \ne {x_2}\), then the function is;

\(\begin{aligned}2{x_1} &\ne 2{x_2}\\2{x_1} - 3 &\ne 2{x_2} - 3\\f\left( {{x_1}} \right) &\ne f\left( {{x_2}} \right)\end{aligned}\)

So, the given function is a one-to-one function.