domain/range of the inverse of the given function f(x)=7-x^2 ; x greater than or equal to 0

Question

domain and range

Answer 1

Given function f(x) = 7-x^2

y = 7-x^2

Inverse of f(x) = x

y = 7-x^2

Subtract 7 from each side.

y-7 = 7-7-x^2

y-7 = -x^2

Multiple to each side by negitive sign.

-y+7 = x^2

x = Sqrt(-y+7)

Domain of the function is the set of all possible values of x and range is the set of all possible values of y.

In the inverse function squre root is involved , negitive squre root is not possible.

So y ≤ 7 range is [-∞,7]

x = Sqrt(-y+7) ≥ 0

Domain is [0,∞]