Answer:
f^-1(x) = 4x^2 -3 . . . . x ≤ 0
Step-by-step explanation:
Interchange x and y, then solve for y.
x = -1/2√(y+3)
-2x = √(y +3)
4x^2 = y +3
4x^2 -3 = y
Note that the range of the function f(x) is f(x) ≤ 0, so this will be the domain of the inverse function. Then the inverse function is ...
f^-1(x) = 4x^2 -3 . . . . for x ≤ 0
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The attached graph shows this inverse function is a reflection of the function across the line y=x, as it should be.
