Let f(x) = x2 – 4, x < 0. What is f-1?Question 3Select 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?
Select one:
- a. -√(x – 4)
- b. -√(x – 4), x > 4
- c. -√(x + 4)
- d. -√(x + 4), x > -4
- e. 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 y and solve for y.
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
Step 4: Take the square root of both sides: √(x + 4) = y
Therefore, the inverse function of f(x) = x^2 - 4 is f^(-1)(x) = √(x + 4).
Among the given options, the correct answer is d. -√(x + 4), x > -4.
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