Question

X

f(x)
-6
12
-3
f(f(1)) =
f-1
ƒ−¹
9
(ƒ−¹ (−3))
0
1
=
1
-3
4
-5
Let f be a continuous and decreasing
function with selected values in the
table above. Let f-¹ be the inverse of
f
9
-6

Answer 1

The question involves understanding and applying the concepts of continuous, decreasing functions and their inverses, but without sufficient information to evaluate f(f(1)), we cannot provide an explicit answer. Instead, we can discuss properties of these functions to assist with the student's comprehension.

Step-by-step explanation:

The question pertains to the concept of functions in mathematics, specifically dealing with a continuous and decreasing function and its inverse. The student is asked to evaluate the expression f(f(1)), given the function and its selected values, which we don't have enough information to solve directly.

However, we can discuss the properties of continuous and decreasing functions, as well as inverse functions, to aid understanding. Continuous functions do not have any breaks or holes, and a decreasing function is one where as the input value increases, the output value decreases.

If a function is decreasing and continuous, and we have the point (x, f(x)), its inverse function f-1 will give us the point (f(x), x) when evaluated at f(x). Similarly, for the inverse function table value of (9, -6), evaluating f-1(-3) would result in 9. In general, the probability P(0 < x < 12) for a continuous probability function means finding the likelihood that a value of 'x' falls within that range, assuming a uniform distribution if not indicated otherwise by the function's behavior.