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- anonymous

graph and find the inverse of f(x)=2x^2-4. Once you find the inverse, graph it too.

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- anonymous

graph and find the inverse of f(x)=2x^2-4. Once you find the inverse, graph it too.

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- zzr0ck3r

This only has a restricted inverse since the function is not 1-1

- anonymous

too bad it doesn't have an inverse ...

- zzr0ck3r

and what I mean is that it does not have an inverse :)

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- anonymous

Hmm..so would I just graph f(x)=2x^2-4 and then say it doesnt have an inverse?

- zzr0ck3r

You can say that by the definition of an inverse, it must be 1-1 and it is not.

- anonymous

Thanks :)

- zzr0ck3r

or I guess graph it and draw a horizontal line through any two points to show it is not 1-1

- anonymous

What about y=-3x+6?
I got -x+3/6 as the inverse

- zzr0ck3r

hmm

- zzr0ck3r

\(y=-3x+6\)
Switch the \(x\) and the (y\) and solve for \(y\).
\(x=-3y+6\\
x-6=-3y\\
\dfrac{x-6}{-3}=y\\
y=\dfrac{6-x}{3}\)

- anonymous

not to butt in but you can still solve
\[2y^2-4=x\]for \(y\) to find an inverse, it just won't be a function

- zzr0ck3r

or restrict the domain on the first one

- anonymous

add 4, divide by 2 and you get
\[y^2=\frac{x+4}{2}\] but when you solve for \(y\) you get
\[y=\pm\sqrt{\frac{x+4}{2}}\]

- anonymous

the \(\pm\) make it not a function

- zzr0ck3r

\(f:\mathbb{R}^+\rightarrow R, f(x) = 2x^2-4\) has as its inverse a proper function.

- zzr0ck3r

I think they meant, use the graph to determine if it has an inverse.

- anonymous

Thanks guys:D

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