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.