Solving f'(x)= f^(-1)(x) [the inverse of f(x)] [Math Mondays]

An illustration of a very powerful technique in problem solving. Helpful in both Math and Software.

Jan 17, 2023

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I’m about to share an amazing video with you.

The video solves an interesting Math Problem-

f'(x)= f(^-1) (x)

If you need a refresher on the symbols, the question wants us to find a function where the function’s derivative is equal to its inverse. If these terms don’t sound familiar to you, go back to my Math for Computer Science post and study the concepts there. Why am I sharing this problem with you?

The solution to this problem utilizes the same patterns, principles, and problem-solving techniques that you will find useful in competitive programming, Leetcode Interviews, and software engineering skills. As I’ve talked about repeatedly in this newsletter/my content- Math and Coding work very similar neural pathways. This is why people with a Math Background have an easier time coding (and why most job postings say Computer Science OR Math in their education requirements). Working on Math Problems will directly improve your Coding Skills (especially for Leetcode-style interviews). If you want to improve in Interviews or Coding, don’t miss this.

These are comments on a video explaining the sliding window technique. Notice that the first comment mentions steps that are identical to the steps I suggest using when learning new concepts/ideas.

Before you proceed, try to solve the problem yourself. This will really strain your mental muscles. Once you’re done/have given up, read on.

The Important Steps in this Video

As you watch the video, I want you to notice the following things-

Solve a Warm-Up Problem First- Micheal starts the problem by finding a warm-up problem, which is significantly easier than the main problem. Anyone who has read many of the solutions here should recognize this step right away. Just to drill home effective this technique is, take a look at the words of one of the people who worked with me in the past. This student was terrified of Leetcode Interviews. Now they are leading a team at a Tech Giant.
I can’t claim all the credit for the student’s results, but building-up is an overlooked technique that can boost your results.
Quick Problem Solving relies on pattern Matching- The way Micheal quickly runs through options might seem magic to you. But it is something that all of you do very well- pattern matching. If you’re struggling with a certain Data Structure or Algorithm- start exposing yourself to a lot of questions about that DS/A. Specifically, stick to the Easy Questions, which will let you build pattern-matching skills. As I’ve covered here, Easy Questions are the most important type of question that you should be working with for learning an idea.
Attack a Problem from multiple angles- Notice how many different ideas are pulled in to create the final solution. It’s not enough to master one idea in isolation. You’re much better off seeing how different ideas interact with each other. This will build much deeper intimacy with these ideas.
Complex Solutions can have simple building blocks- None of the ideas used in the articles are really that high-level. The concepts needed to solve it are mostly high-school level. This question isn’t hard because you need to know a lot. This question is hard because you need to use what you know. In fact, many higher-level math/computer science solutions are very similar to this. This is why there is so much value in learning the basics. They will show up everywhere.

With all that out of the way, take a look at the video. How did you do? Let me know by replying to this email/post/using my social media links to reach out to me.

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