Which function below is the inverse

Question

of f(x) = x^2 − 16?

Answer 1

First apply horizontal line test :

The graph of the function given by f(x) = x² - 16 is shown in the above the Figure . Because it is possible to find a horizontal line that intersects the graph of f(x) at more than one point, can conclude that f(x) is not a one-to-one function and does not have an inverse function.

The function is not a function.

Find the inverse function of  f(x) = x² - 16 when x ≥ 0.

Replace f(x) by y.

y = x² - 16

Inter change x and y.

x = y² - 16

Solve for y.

x + 16  = y²

y = ± √(x + 16)

y = √(x + 16), since x ≥ 0.

Replace y by f ^{- 1}(x).

f ^{- 1}(x) = √(x + 16)

The inverse of function of  f(x) = x² - 16 ( x ≥ 0 ) is f ^{- 1}(x) = √(x + 16).