Let f ( x ) = ( x + 3 ) ^2
1 answer:
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.
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