Question

Let f ( x ) = ( x + 3 ) ^2

Answer 1

Answer:

  f(x) restricted to x in [-3, ∞) will have inverse function f⁻¹(x) = √x -3

Step-by-step explanation:

The given function is non-decreasing on the interval [-3, ∞), so that is a suitable domain.

The inverse function can be found from ...

  x = f(y) = (y +3)^2

  √x = y +3

  √x -3 = y

So, the inverse function of f(x) on the domain [-3, ∞) is ...

  f⁻¹(x) = √x -3

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In the attached graph, the solid red curve is the domain-restricted portion of f(x). The blue curve is the inverse function. The dashed orange line is a reference line to help you see that the inverse function is a reflection of the function across that line.