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

1. zzr0ck3r

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

2. anonymous

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

3. zzr0ck3r

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

4. anonymous

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

5. zzr0ck3r

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

6. anonymous

Thanks :)

7. zzr0ck3r

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

8. anonymous

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

9. zzr0ck3r

hmm

10. zzr0ck3r

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

11. 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

12. zzr0ck3r

or restrict the domain on the first one

13. anonymous

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

14. anonymous

the $$\pm$$ make it not a function

15. zzr0ck3r

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

16. zzr0ck3r

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

17. anonymous

Thanks guys:D