Which is the correct answer?

(explain how you got your answer)

Option B. f¯¹(x) = ³√(– x – 9)

Step-by-step explanation:

From the question given above:

f(x) = – x³ – 9

f¯¹(x) =?

We can obtain the inverse f¯¹(x) of the above equation by doing the following:

f(x) = – x³ – 9

Replace f(x) with y

y = – x³ – 9

Interchange x and y

x = – y³ – 9

Make y the subject . This is illustrated below:

x = – y³ – 9

Rearrange

x + 9 = – y³

Multiply through by –1

–(x + 9) = y³

y³ = – x – 9

Take the cube root of both side

y = ³√(– x – 9)

Replace y with f¯¹(x)

f¯¹(x) = ³√(– x – 9)

Thus, the inverse of the function

f(x) = – x³ – 9

is

f¯¹(x) = ³√(– x – 9)

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