# How to determine whether f(x)= 2x²-4x -1 is one to one function given that x is more than or equal to 1?

##### 3 Answers

So

#### Explanation:

This is a parabola with vertex at

If

by directly solving. So

#### Explanation:

So if

Add

Divide both sides by

So:

Given

So

Add

So

This can also be determined graphically.

#### Explanation:

The graph of

(Use the vertex formula or put the expression in vertex form:

So with no restriction on the domain, the graph looks like:

graph{2x^2-4x-1 [-6.97, 10.81, -5.69, 3.2]}

With its natural domain for the expression, the function

When we restrict the domain to

The graph of

graph{y = (2x^2-4x-1)*sqrt(x-1)/sqrt(x-1) [-4.32, 8.17, -4.367, 1.88]}

This function passes the horizontal line test. It is one-to-one.