Question

Find f-1(x) for the function: f(x) = -x^2 - 7.

A) f-1(x) = -√(x + 7)
B) f-1(x) = √(-x + 7)
C) f-1(x) = -√(x - 7)
D) f-1(x) = √(-x - 7)

Answer 1

To find the inverse of the function f(x) = -x^2 - 7, swap the roles of x and y, solve for y, and simplify the expression.

Step-by-step explanation:

Answer:

To find the inverse of the function f(x) = -x^2 - 7, we need to swap the roles of x and y and solve for y. Here are the steps:

1. Replace f(x) with y: y = -x^2 - 7
2. Swap x and y: x = -y^2 - 7
3. Solve for y: -y^2 - 7 = x
4. Add 7 to both sides: -y^2 = x + 7
5. Multiply by -1 to get rid of the negative sign: y^2 = -x - 7
6. Take the square root of both sides: y = ±√(-x - 7)

The inverse function is given by f-1(x) = ±√(-x - 7).

Therefore, the correct answer is D) f-1(x) = √(-x - 7).