# 1. Introduction

If a function can undo the operation of any other function then the function that “undo” another function is called the inverse function of that function. The inverse function of a function f(x) is denoted by “f^{-1}(x)”. To be an inverse function the function needs to be Onto and One-One. For example, if a function f(x) = 3x, which triples the number which is provided as input, then the inverse of this function has to make it one third to get the input back. Therefore, f^{-1}(x) = x/3. Two functions g(x) and f(x) are inverses of one another, then “g(x) = y only if f(y)=x”.

g(f(x)) = x.

This report on the use of inverse function in information technology is discussed with the help of three pieces of literature. Then a flowchart has been created to implement the application of inverse function in computer programs. An algorithm is developed for the inverse and then test it for two inputs.

# 2. References of three articles

- Ikram, M., Susanto, H. and Purwanto, I., 2020, August. Did Undergraduate Students Really Establish Reversible Reasoning When Faced With Inverse Function Problem Situations?. In
*SEMANTIK Conference of Mathematics Education (SEMANTIK 2019)*(pp. 27-33). Atlantis Press. Available from: https://www.atlantis-press.com/article/125944183.pdf [Available at: 10/05/2022] - Lawson, J., 2020. An inverse function theorem converse.
*Journal of Mathematical Analysis and Applications*,*486*(2), p.123913. Available from: https://arxiv.org/pdf/1812.03561 [Available at: 10/05/2022] - Emmanuel Eziokwu, C., 2020. On The Inverse Function Theorem and its Generalization in the Unitary Space.
*Asian Journal of Mathematical Sciences*. Available from: https://www.researchgate.net/profile/Emmanuel-Eziokwu/publication/346443810_On_The_Inverse_Function_Theorem_and_its_Generalization_in_the_Unitary_Space/links/5fc24ac0a6fdcc6cc6782463/On-The-Inverse-Function-Theorem-and-its-Generalization-in-the-Unitary-Space.pdf [Available at: 10/05/2022]

# 3. Literature review

- Ikram
*et al.*2020 investigate reversible reasoning, especially the mental actions of students in the problem-solving of an inverse function. The reversible thinking of several high-achieving students at the undergraduate level is compared in this given scenario. These students had previously been examined on their comprehension of component functioning. Data gathered via think loudly and clinical conversations indicate tactics employed by respondents in order to trace directly to the original function. When dealing with inverse function issues, 3 undergraduate students demonstrate diverse reversible logic models, which include reversible inflexible, analytical, and divergent strategies. Further research on strengthening the understanding and legitimacy of bidirectional reasoning as an important tool for students and teachers in classroom practice is suggested. - Lawson (2020) established a convers function of the well-known inverse function theorem. If “g: U V and F: V U” be the homeomorphisms among the open subsets of the Branch spaces. If function g is differentiable at class and function f is locally Lipschitz, then Frechet Derivative of g at every point of the U is invertible as well as f have to be differentiable at class .
- According to Emmanuel Eziokwu (2020), the inverse function theorem influence the Branch space for R. this paper mainly focus on the concept of inverse function theorem. This theory mainly helps to detect that the inverse function able to hold Rn. the unitary space mainly holds the establishment process that can extend to Cn. It will help to generalize the unitary space.

# 4. Application in information technology

There are various applications of inverse function in information technology. With the help of the concept of the inverse function, various data and information can be traced (Stănică and Geary, 2021). By applying inverse function in the information technology cause can be deduced from the effect. The inverse function can be used in machine learning, computer vision, medical imaging, and remote sensing.

**Imaging**

With the help of the concept of an inverse function, an original image can be generated. The mapping of an image to quantities from the quantities is known as the forward problem. With the help of different physical theory, the details of the forward problem can be found. The mapping of actual data from the image is given through the relation Y = A(x) + n. Then the inverse problem is the findings of the original image from knowledge of forward problem and given data. For example with the help of inverse function in information technology, an original image can be found from a blurred or damaged image.

# 5. Description of this choice

The inverse function is not only confined to the mathematics or computer language, it has a different use in everyday life. From real-life activity to the technology can activity it has a significant application. In our daily life, there are different activities that can be explained and solved through the inverse function, such with the help of the inverse function temperature of an object is possible to change from Fahrenheit to Celsius or vice versa. For the huge application of inverse function in real life and how it is applied in information technology to deduce the cause from effect, the universe function has been chosen for this report.

# 6. Flowchart

Let a function f(x) = 3x + 5, then the below diagram represents the flow chart of inverse function of f(x) i.e. f^{-1}(x).

**Figure 1: Flow chart**

(Source: self-created in draw.io)

# 7. Algorithm

- Replace f(x) by y
- Swap y and x
- Solve for y
- Replace y with f
^{-1}(x)

# 8. Algorithm test

1) Input , f(x) = 3x + 5

Step 1: y = 3x +5

Step 2: x = 3y +5

Step 3:

3y = x-5

Or, y = (x-5)/3

Step 4: f^{-1}(x) = (x-5)/3

2) Input = f(x) = 4x -2

Step 1: y = 4x -2

Step 2: x = 4y – 2

Step 3:

4y = x + 2

Y = (x+2)/4

Step 4: f^{-1}(x) = (x+2)/4

# 9. Conclusion

The function which undoes the operation of a function is called the inverse function. To get the inverse function one function has to be bijective and onto. In information technology, the inverse function has several uses. Various data and information may be tracked using the notion of the inverse function. An original picture can be recovered from a blurred or damaged image using the inverse function in information technology. The universe function was chosen for this research because of the vast use of the inverse function in real life and how it is used in information technology to discern cause from effect.

# 10. Statement about group contribution

Within a group, we need to be participative. Participation in the group will help to develop my team management skills. I need to be specific with my work. If required help I need to ask for help from my team. I need to focus on building good communication with the team.

# References

**Journals**

Aaftab V, M. and Sharma, M., 2021. OGGN: A Novel Generalized Oracle Guided Generative Architecture for Modelling Inverse Function of Artificial Neural Networks. *arXiv preprint arXiv:2104.03935*.

Emmanuel Eziokwu, C., 2020. On The Inverse Function Theorem and its Generalization in the Unitary Space. *Asian Journal of Mathematical Sciences*.

IKRAM, M., PARTA, I.N. and SUSANTO, H., 2020. Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics. *Journal for the Education of Gifted Young Scientists*, *8*(1), pp.591-611.

IKRAM, M., PARTA, I.N. and SUSANTO, H., 2020. Exploring the Potential Role of Reversible Reasoning: Cognitive Research on Inverse Function Problems in Mathematics. *Journal for the Education of Gifted Young Scientists*, *8*(1), pp.591-611.

Lawson, J., 2020. An inverse function theorem converse. *Journal of Mathematical Analysis and Applications*, *486*(2), p.123913.

Stănică, P. and Geary, A., 2021. The c-differential behavior of the inverse function under the EA-equivalence. *Cryptography and Communications*, *13*(2), pp.295-306.