You are here:

Calculus/Composite functions


I am currently learning about composite functions,  My text book has the following problem : (fofg)(x) where f(x)=x^2+3x-1 and g(x)=2x-3.  The answer the book is giving me is 4x^2+12x+9+6x+9-1.  Where does the 12x come from?

Is (fofg)(x) really suppose to be (fog)(x)?

What that means is to take g(x) and put it in as the x's in f(x).

It seems clearer to say that f(y) = y+3y-1 and g(x) = 2x-3.
What (fog)(x) is can be found by finding f(y) where y = g(x).
In other words, take y = 2x - 3.

With y = 2x - 3 put into y+3y-1 gives (2x-3)+3(2x-3)-1.
Now (2x-3) is 4x - 12x + 9 and -3(2x-3) is -6x + 9.

Putting both of these terms into  (2x-3) + 3(2x-3) - 1 gives 4x - 12x + 9 - 6x + 9 - 1.

To me it looks like a misprint, for to get this answer, we need g(x) = 2x + 3
{note the '+ 3' instead of the '- 3'}.  That would make the -12x into +12x and the -6x into +6x.

Note that the x terms can be combined, since -12x - 6x = -18x { or 12x + 6x = 18x}.
Also, the constants can be combined, since 9 - 1 = 8.


All Answers

Answers by Expert:

Ask Experts




Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology (reproduction, insusion of chemicals into bloodstream).


Experience in the area: I have tutored students in all areas of mathematics since 1980. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Maybe not a publication, but I have respond to well oveer 8,500 questions on the PC. Well over 2,000 of them have been in calculus.

I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few courses at college a year early.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

©2017 All rights reserved.