Reversed Composite Function

Featured problem for today was taken from EMC blitz Quiz organized by one of the members of the active group in facebook called Elite Math Circle. It is about composite function but the problem is reversed. It is very easy at first glance but a bit hard and confusing to solve.




If (f\circ g)(x)=\displaystyle\frac{1}{x-25} and f(x)=x^2+5, find g(x).


(f\circ g)(x)=f(g(x)) \displaystyle\frac{1}{x-25}=(g(x))^2+5 (g(x))^2=\displaystyle\frac{1}{x-25}-5 (g(x))^2=\displaystyle\frac{1-5(x-25)}{x-25} (g(x))^2=\displaystyle\frac{-5x+126}{x-25}

Extracting the squares of both sides,






Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

Latest posts by Dan (see all)

You may also like...

5 Responses

  1. Courtney says:

    I’m not sure why but this web site is loading very slow for me. Is anyone else having this issue or is it a issue on my end? I’ll check back later on and see if the problem still exists.

  2. forever live says:

    Thank you for the good writeup. It in fact was a amusement account it. Look advanced to far added agreeable from you! However, how could we communicate?

  3. Excellent publish from specialist also it will probably be a fantastic know how to me and thanks really much for posting this helpful data with us all.

  4. Youre so cool! I dont suppose Ive read anything in this way before. So good to uncover somebody with some original tips on this topic. realy appreciate starting this up. this excellent website is something that is necessary more than the internet, a person if we do originality. valuable function for bringing something new towards the web!

  5. Brent Wiesen says:

    Thank you of this blog. That’s all I’m able to say. You undoubtedly have made this web web site into an item thats attention opening in addition to critical. You certainly know a fantastic deal of about the niche, youve covered a multitude of bases. Fantastic stuff from this the main internet. All more than again, thank you for the blog.

Leave a Reply

Your email address will not be published. Required fields are marked *