Question

Determine whether the function\(f(x) = {x^2} - 2x\)is one-to-one.

Short answer

The function \(f(x) = {x^2} - 2x\) is not a one-to-one.

Step-by-step solution

Given data

The given function is\(f(x) = {x^2} - 2x\).

Concept of functions

The simplest definition is an equation will be a function if, for any \({\rm{x}}\) in the domain of the equation (the domain is all the \({\rm{x}}\)'s that can be plugged into the equation), the equation will yield exactly one value of \({\rm{y}}\) when we evaluate the equation at a specific \({\rm{X}}\).

Simplify the expression

Perform the horizontal line test to check whether the function \(f(x) = {x^2} - 2x\) is not a one-to-one.

Sketch the graph of the function \(f(x) = {x^2} - 2x\) and perform the horizontal line test.

From Figure, it is observed that the horizontal line intersects the curve exactly at two points, which means it does not pass the horizontal line test.

Therefore, the function \(f(x) = {x^2} - 2x\) is not a one-to-one.