Question

PLEASE HELP!!

The domain of a function f(x) is x <_ 0, and the range is y <_-1. What are the domain and range of its inverse function, f-1(x)?

Answer 1

Option D.

Explanation:

Domain and range of inverse function:

The domain of the inverse function(x values) is the range(y values) of the original function.

The range of the interse function(y values) is the domain of the original function(x values).

Original function:

Domain:
`x \geq 0`

Range:
`y \leq -1`

Inverse function:

x values in the domain of the inverse function are the y values in the range of the original function. So

Domain:
`x \leq 1`

Same for range(exchange of y and x).

Range:
`y \geq 0`

The answer is given by option D.