Another Function problem! (more difficult)

[Guest]

Find f(x) if f ( f(x) - x^2 ) = 2x^2+ 4x + 3

 

[tkhunny]

Assume f(x) = a*x^2 + b*x + c
Find f(f(x)-x^2)
Equate coefficients.
Solve for a, b, and c.

It's just a legwork problem.

When you are done, you will see that there is an easier way.

 

[Guest]

About Function!

I think, if we assume that f(x) = a*x^2+bx+c
Then we will get f(f(x)) in the form of 4 order equation because
f(f(x)) = a(ax^2+bx+c)^2+b(ax^2+bx+c)+c
= ...x^4+.....
So your answer is wrong

 

[tkhunny]

Re: About Function!

I think, if we assume that f(x) = a*x^2+bx+c
Then we will get f(f(x)) in the form of 4 order equation because
f(f(x)) = a(ax^2+bx+c)^2+b(ax^2+bx+c)+c
= ...x^4+.....
So your answer is wrong

Arrogance! Very nice. I don't get that very often.

Don't count your Order before your Parameters hatch.

If the coefficient on x^4 is zero (0), does that make it a quartic equation?

One of the things we teach in mathematics is thinking, rather than jumping to rash conclusions. Nice try, though. I think you overlooked my promise that it would get easier AFTER you do what I told you. Come on. Give it a try. :wink: Actually, it's kind of obvious, but I thought I'd make you go through the algebra exercise.