Question

Given the function \(f(x) = -x - 5\), find the inverse of \(f(x)\) and write it in proper function notation.

a) \(f^{-1}(x) = -x + 5\)
b) \(f^{-1}(x) = -5x\)
c) \(f^{-1}(x) = x - 5\)
d) \(f^{-1}(x) = \frac{1}{x + 5}）

Answer 1

To find the inverse of the function f(x) = -x - 5, swap x and y and solve for y to get f^{-1}(x) = -x + 5, which is option a).Therefore, the correct answer is a) f^{-1}(x) = -x + 5.

Step-by-step explanation:

To find the inverse of the function f(x) = -x - 5, you need to perform the following steps:

1. Replace f(x) with y: y = -x - 5.
2. Swap x and y: x = -y - 5.
3. Solve for y: adding 5 to both sides gives x + 5 = -y, and then multiply by -1 to get -x - 5 = y.
4. Rewrite the equation with inverse notation: f^{-1}(x) = -x + 5.

Therefore, the correct answer is a) f^{-1}(x) = -x + 5.