Question

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

Answer 1

`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`)