This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.

For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Determine whether the function given is invertible or non-invertible.

Using technology to graph the function  results in the following graph.

This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.

Step 2: Make the function invertible by restricting the domain.

To make the given function an invertible function, restrict the domain to  which results in the following graph.

Step 3: Graph the inverse of the invertible function.

Swapping the coordinate pairs of the given graph results in the inverse.

Therefore, the inverse of this function algebraically is

This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship. 

For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify the information that is given in the question.

Step 3: Use algebraic methods to state mathematical relationships and produce function.

Using the steps outlined above is as follows.

Step 1: Identify what the question is asking for.

This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.

Step 2: Identify the information that is given in the question.

Initial amount of blooms prior to introducing the fertilizer is two.

The fertilizer doubles the blooms every day. If  is representing days then the rate of the blooms is, 

 .

Notice that this question is talking about a growth rate therefore, we can use the following formula.

The number of blooms that form after the fertilizer is introduced is two every day. Therefore,

Step 3: Use algebraic methods to state the mathematical relationship and produce the function.

Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.