Let f(x) = – x2 – 4, x < 0. What is f-1?Question 4Select one:a.–√(–x – 4)b.–√(–x – 4), x < – 4c.√(x + 4)d.–√(–x – 4), x > – 4e.None of these
Question
Let f(x) = – x2 – 4, x < 0. What is f-1?Question 4Select one:a.–√(–x – 4)b.–√(–x – 4), x < – 4c.√(x + 4)d.–√(–x – 4), x > – 4e.None of these
Solution
To find the inverse of the function f(x) = -x^2 - 4, we need to switch the roles of x and f(x) and solve for x.
Step 1: Replace f(x) with y. y = -x^2 - 4
Step 2: Swap x and y. x = -y^2 - 4
Step 3: Solve for y. x + 4 = -y^2 y^2 = -x - 4
Step 4: Take the square root of both sides. y = ±√(-x - 4)
Therefore, the inverse of f(x) is f^(-1)(x) = ±√(-x - 4).
The correct answer is e. None of these.
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