Lf g(x) is the inverse of f(x), what is the value of f(g(2))?​

Further explanation

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.,  

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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.

Learn more

The inverse of a function

The piecewise-defined functions

The composite function

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

Step-by-step explanation:

2

a reflection across the x axis and a 90 degree rotation left and right.