Question

Find the inverse of the given function

Answer 1

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.