Question

Function f, graphed below, is NOT an invertible function.

To which intervals could we restrict the domain of f to make it an invertible function?
Choose all answers that apply:

A. 1 ≤ x ≤ 6
B. 0 ≤ x ≤ 8
C. -8< x < -4

Answer 1

The answer would be B

Answer 2

The intervals to which we could restrict the domain of f to make it an invertible function are;

A. 1 ≤ x ≤ 6

B. 0 ≤ x ≤ 8

C. -8 < x < -4

In Mathematics and Euclidean Geometry, an invertible function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

Generally speaking, an invertible function never repeats its output values, which ultimately implies that its inverse would be a function too.

By critically observing the graph shown above, we can logically deduce that the domains for which the given function f have only one input value per output value include;

Over the domain (interval) 1 ≤ x ≤ 6, the given function f is strictly decreasing and continuous. Hence, there is exactly one input value for every output value over that interval.

Similarly, the given function f is strictly decreasing and continuous over the domain (interval) 0 ≤ x ≤ 8. So, there is exactly one input value for every output value over that interval.

In conclusion, the given function f is strictly increasing and continuous over the domain (interval) -8 < x < -4. So, it is an invertible function because there is exactly one input value for every output value over that interval.