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.,  

- - - - - - -

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

step-by-step explanation:

first you will have to convert 3/4 into a decimal

which is .75

then you will have to divide 1.5 by .75

which is 2

no you have to divide

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt