If g(x) is the inverse of f(x), what is the value of f(g(

a. -6
b. -3
c. 2
d. 5

2

Given:

g(x) is the inverse of f(x)

Question:

What is the value of

The Process:

The formal definition for the inverse of a function:

Let f be a one-to-one and onto function with the domain A and the range B. Then its inverse function has the domain B and the range A such that

By definition the inverse function undoes what does. That is, if we take , apply , and the apply , we arrive back at where we started. Similarly,   undoes what does. That is why are the inverses of each other.

Note:

In other words,

Let's get back to our problem.

Given that is the inverse of We write as follows:

We prepare the composite function of

Substitute into the composite function.

Thus becoming,

We calculate the value of rewritten to

Therefore we get the answer, i.e.,  

- - - - - - -

Note:

To find the inverse, we use the same procedures that we used for relations. Drawing the reflection with respect to we get the following picture as in the attachment. We can also discover proof of this problem in the attached picture.

Keywords: g(x) is the inverse of f(x), what is the value of f(g(2))?, the composite function, one-to-one and onto function, with the domain A and the range B, y = x, the reflection