How do you find the inverse of f(x)=2-2x^2?

1 Answer
Jan 24, 2016

f^-1(x)=sqrt{(2-x)/2}

Explanation:

The function if defined as f(x)=y then the inverse would be f^-1(y)=x

Now, given f(x)=2-2x^2 so y=2-2x^2
Subtracting by 2 on both sides and then multiplying by -1 we get
2-y=2x^2,
let's divide by 2 now.
So, (2-y)/2=x^2 Now, taking the square root, we get
\sqrt{(2-y)/2}=x and if you see above, f^-1(y)=x.
So the answer is as given above. (just replace y with x)