Find the inverse.
y=2 square root 5 x^3+5

Question

anonymous · Answer

$$y=2\sqrt[5]{x^3+5}$$

anonymous · Answer

I thought you were supposed to switch x and y first?

anonymous · Answer

Fair enough. We are used to doing it differently but the results are the same. So switch x & y. Then you'll need to isolate y.

jhannybean · Answer

First checkif this function passes the horizontal line test for all values of x, and whether or not it is 1 to 1.

anonymous · Answer

$$x/2=\sqrt[5]{y^3+5}$$

anonymous · Answer

Great. Now to get rid of the 5th root. What's the inverse operation of taking the 5th root?

anonymous · Answer

$$(x/2)^5=y^3+5$$

anonymous · Answer

Terrific. Now get rid of the 5 by subtracting from both sides.

anonymous · Answer

$$(x/2)^5-5=y^3$$

anonymous · Answer

Right on. Now solve for y. What's the inverse operation of raising a number to exponent 3?

anonymous · Answer

$$\sqrt[3](x/2)^5-5=y$$

anonymous · Answer

Excellent. Don't forget to take the cube root of everything on the left hand side. Well done.

anonymous · Answer

$$\sqrt[3]{\left( \frac{ x }{ 2 } \right)^5-5}=y$$

anonymous · Answer

Thank you! Do you think you could help me with one more? It's easier than this one.

anonymous · Answer

I'm terribly sorry. I have to run right now. But there's lots of great people on here to help you. Good. luck.