Question

Consider the function f(x) = x + 5 - 7 for the domain (-5, -0). Find f'(x), where f' is the inverse of f. Also state the domain in interval notation.

a) f'(x) = x + 2, domain: (-5, -0)
b) f'(x) = x - 2, domain: (-5, -0)
c) f'(x) = x + 12, domain: (-5, -0)
d) f'(x) = x - 12, domain: (-5, -0)

Answer 1

a) f'(x) = x + 2, domain: (-5, -0). To find the inverse of the function f(x) = x + 5 - 7, switch the roles of x and f(x) and solve for x. The inverse function f'(x) is f'(x) = x + 2, with a domain of (-5, -0).

Step-by-step explanation:

To find the inverse of the function f(x) = x + 5 - 7, we need to switch the roles of x and f(x) and solve for x. So, let y = x + 5 - 7. Rearranging the equation, we get x = y - 5 + 7 = y + 2.

Therefore, the inverse function f'(x) is f'(x) = x + 2.

The domain of f(x) is (-5, -0), which means that the domain of f'(x) is also (-5, -0).

Therefore, the correct option is a) f'(x) = x + 2, domain: (-5, -0).