Question

Let f(x)=(x+2)^(2) Find a domain on which f is one -to-one and non -decreasing. Find the inverse of f restricted to this domain. f^(-1)(x)

Answer 1

Explanation:

The domain of a quadratic is All Reals however the function is only increasing on the interval (-2, ♾️)

Therefore the domain is (-2, ♾️). The function is also one to one since only one. x value maps to one y value.

`y = (x + 2) {}^(2)`

Swap x and y

`x = (y + 2) {}^(2)`

`√(x) = y + 2`

`√(x) - 2 = y`

Let y=f^-1(x)

`f {}^( - 1) (x) = √(x) - 2`

The domain here is [0, ♾️)

It won't be all reals since we can not graph the square root of a negative number on a cartisean coordinate plane