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Find the inverse of the function π(π₯) = β(2 β π₯).

Find the inverse of the function π of π₯ equals the cube root of two minus π₯.

The first thing we wanna do is replace π of π₯ with π¦. Now weβre going to interchange π₯ and π¦. So π₯ is equal to the cube root of two minus π¦, and now we will solve for π¦.

So the first thing that we need to do is to cube both sides to get rid of the cube root. So now we have π₯ cubed equals two minus π¦. So letβs first subtract two to both sides. So we have π₯ cubed minus two is equal to negative π¦. Now we wanna isolate π¦ and get it by itself. So letβs go ahead and divide by the negative one everywhere. Essentially, weβre just changing the sign on every term. So we have π¦ equals negative π₯ cubed plus two. Or it could be written as π¦ equals two minus π₯ cubed.

And now we replace π¦ with π inverse π₯, so the inverse of our function would be two minus π₯ cubed.

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