Question

Need help plsssss ....................................................

Answer 1

`f^(-1)(x) = \pm√(x) + 2`

Explanation:

To find the inverse of a function, we can list out the operations done unto x and invert their opposites.

The operations for the function f(x) = (x − 2)² are:

1. subtract 2
2. square

So, the operations for its inverse function will be:

1. square root
2. add 2

Finally, we can represent this in equation form:

`f^(-1)(x) = √(x) + 2`

However, since there is a domain restriction on the principal square root function, we have to add a ± sign in front of the
`√(x)`.

`\boxed{f^(-1)(x) = \pm√(x) + 2}`

Further Note

Additionally, we know that x must also be positive or 0, as negative numbers do not result in a real output when square rooted, though putting a function's inherent domain restriction after the its definition is not always necessary:

`f^(-1)(x) = \pm√(x) + 2, \ x \ge 0`