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

Question

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

zzr0ck3r · Answer

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

anonymous · Answer

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

zzr0ck3r · Answer

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

anonymous · Answer

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

zzr0ck3r · Answer

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

anonymous · Answer

Thanks :)

zzr0ck3r · Answer

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

anonymous · Answer

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

zzr0ck3r · Answer

hmm

zzr0ck3r · Answer

$y=-3x+6$

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 · Answer

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 · Answer

or restrict the domain on the first one

anonymous · Answer

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 · Answer

the $\pm$ make it not a function

zzr0ck3r · Answer

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

zzr0ck3r · Answer

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

anonymous · Answer

Thanks guys:D