MHB Understanding inverse functions

AI Thread Summary
The function f(x) = 3(x + 1)^2 - 12 does not have an inverse because it is a parabola that fails the horizontal line test, meaning that horizontal lines intersect the graph at more than one point. This indicates that for some values of y, there are multiple corresponding x values, violating the requirement for a function to have a unique inverse. The domain of the function is restricted to {-3 < x < 1}, but this does not change the fundamental property of the parabola. Understanding that a function must be one-to-one to possess an inverse is crucial. Therefore, despite being a parabola, the function does not meet the criteria for having an inverse.
Casio1
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I have a graph f(x) = 3(x + 1)^2 - 12 , I have sketched this graph (Not shown) hand it is a parabola with a y- intercept at - 9. the vertex being - 12.

The image set is a closed interval {- 12, infinity} Sorry no square brackets and no sign for infinity.

I am asked to explain why the function of f does not have an inverse?

Given that the graph is a parabola I would have thought that the graph did have an inverse?

The domain {-3 < x < 1}

I am missing something here in the understanding if anyone can advise It would be much appreciated.

Sorry I didn't include a sketch the paint package won't allow me to draw a curve:o
 
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Casio said:
I have a graph f(x) = 3(x + 1)^2 - 12 , I have sketched this graph (Not shown) hand it is a parabola with a y- intercept at - 9. the vertex being - 12.

The image set is a closed interval {- 12, infinity} Sorry no square brackets and no sign for infinity.

I am asked to explain why the function of f does not have an inverse?

Given that the graph is a parabola I would have thought that the graph did have an inverse?

The domain {-3 < x < 1}

I am missing something here in the understanding if anyone can advise It would be much appreciated.

Sorry I didn't include a sketch the paint package won't allow me to draw a curve:o

A function is single valued, so for your f(x) to have an inverse for every y in its range there must be one and only one x in its domain such that y=f(x).

That is every horizontal line y=u that cuts the curve y=f(x) cuts it in one point only.

CB
 
CaptainBlack said:
A function is single valued, so for your f(x) to have an inverse for every y in its range there must be one and only one x in its domain such that y=f(x).

That is every horizontal line y=u that cuts the curve y=f(x) cuts it in one point only.

CB

Thanks CB
 
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