## haleyelizabeth2017 one year ago Find the inverse of f(x). (there are two)

1. haleyelizabeth2017

$f(x)=-4x^2+1$

2. haleyelizabeth2017

Don't I switch f(x) and x to begin with?

3. Nnesha

f(x) is same as y so we can rewrite this as $\huge\rm y=-4x^2+1$ to find inverse switch x and y

4. whpalmer4

and solve for $$y$$

5. Nnesha

yes right

6. jdoe0001

$$\bf f(x)={\color{blue}{ y}}=-4{\color{brown}{ x}}^2+1\qquad inverse\implies {\color{brown}{ x}}=-4{\color{blue}{ y}}^2+1\impliedby f^{-1}(x)$$ yes

7. haleyelizabeth2017

I got: $y=\sqrt{\frac {x-1}{-4}}$

8. Nnesha

hmm $\huge\rm \color{ReD}{x}=-4\color{blue}{y}^2+1$ divide by -4 $\frac{ x-1 }{ -4 }$ is same as $\huge\rm \frac{ x }{ -4 } -\frac{ 1 }{ -4 }$ first divide the sign and then take square root and remember when we take square root we should get 2 solutions $\sqrt{x^2} = \pm x$

9. haleyelizabeth2017

wait, what? Sorry, you lost me there lol

10. Nnesha

$\frac{ x }{ -4 }-\frac{ 1 }{ -4 } = -\frac{ x }{ 4 }+\frac{ 1 }{ 4 }$ -1 divided by -4 = positive 1/4

11. haleyelizabeth2017

oh

12. Nnesha

|dw:1443653401397:dw|

13. Nnesha

hint $\sqrt{\frac{ a }{ b }}=\frac{ \sqrt{a} }{ \sqrt{b} }$

14. haleyelizabeth2017

So, $\frac{\sqrt{-x+1}}{2}$?

15. Nnesha

looks good

16. haleyelizabeth2017

Thank you :)

17. haleyelizabeth2017

Is that all?

18. Nnesha

yes that's it

19. haleyelizabeth2017

Awesome! :) And it is also a function, correct?