Question

If F'(x) is the inverse of F(x), what is the value of Fl(F(x))?

Option 1: x2
Option 2: x
Option 3: 1
Option 4: 0

Answer 1

The value of F'(F(x)) when F'(x) is the inverse of F(x) is x. This is because the inverse function undoes the original function's action, leading you back to the original value.

Step-by-step explanation:

You appear to be asking about the property of inverse functions in mathematics. If F'(x) is the inverse of F(x), then by definition, the inverse function F'(x) will undo the action of F(x). Therefore, if you apply F(x) to some value and then apply its inverse F'(x) to the result, you will end up with the original value you started with.

Mathematically, the application of F'(F(x)) will yield the value x. In function notation, this property is mostly expressed as F'(F(x)) = x for any value of x in the domain of F.

Example

Let's consider an example with a function F(x) = x². Its inverse would be F'(x) = √x. Following the rule above, if we apply the inverse to the function: F'(F(x)) = √(x²), we simplify the square root and the square, which just leaves us with x.