Question Video: Finding the Inverse Function of Radical Functions Mathematics • 10th Grade

Find the inverse of the function 𝑓(𝑥) = ∛(2 − 𝑥).


Video Transcript

Find the inverse of the function 𝑓 of 𝑥 equals the cube root of two minus 𝑥.

The first thing we wanna do is replace 𝑓 of 𝑥 with 𝑦. Now we’re going to interchange 𝑥 and 𝑦. So 𝑥 is equal to the cube root of two minus 𝑦, and now we will solve for 𝑦.

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 𝑥 cubed equals two minus 𝑦. So let’s first subtract two to both sides. So we have 𝑥 cubed minus two is equal to negative 𝑦. Now we wanna isolate 𝑦 and get it by itself. So let’s go ahead and divide by the negative one everywhere. Essentially, we’re just changing the sign on every term. So we have 𝑦 equals negative 𝑥 cubed plus two. Or it could be written as 𝑦 equals two minus 𝑥 cubed.

And now we replace 𝑦 with 𝑓 inverse 𝑥, so the inverse of our function would be two minus 𝑥 cubed.

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