Final answer:
The value of F^1(F(x)) where F^1(x) is the inverse function of F(x) is simply x. This reflects the principle that applying a function and its inverse will result in the original value. The concept mirrors negative exponents, where multiplying a number by its reciprocal (or inverse) gives 1.
Step-by-step explanation:
If F1(x) is the inverse of F(x), then the value of F1(F(x)) is simply x. This is because applying a function and then its inverse results in the original input value. In other words, if you apply a transformation to a value and then apply the inverse transformation, you get back to where you started.
To understand this with exponents, consider the example of negative exponents indicating division. This is analogous to how the inverse function works. A negative exponent such as x-1 is equivalent to 1/x, and when we multiply x by 1/x, we get 1, reflecting the same principle of inverses bringing you back to the original value which in case of functions is the input x.