Given the following functions $f $ $g $ and $h $
such that $f : x \rightarrow 3x+2 $ $g : x \rightarrow x^2 -1 $ and $h : x \rightarrow px+q $ where $x $ is a real number and $p $ and $q $ are constants, such that $ [f o (g o h) ] =3x^2+12x+11 $ . Find the values of $p $ and $q $

Question

Given the following functions $f $ $g $ and $h $
such that $f : x \rightarrow 3x+2 $ $g : x \rightarrow x^2 -1 $ and $h : x \rightarrow px+q $ where $x $ is a real number and $p $ and $q $ are constants, such that $ [f o (g o h) ] =3x^2+12x+11 $ . Find the values of $p $ and $q $

anonymous · Answer

What have you tried saso?

sasogeek · Answer

I could not do this one so it wasn't part of my attempts... i had to choose 12 out of the 15...

anonymous · Answer

Hint : Find $ f o (g o h)  $ using the  definition and then compare coefficient.

anonymous · Answer

You can't use that arrow while defining a function, can you?

anonymous · Answer

Yes Ishaan we can. it's just a fancy way to write $ f(x) $

anonymous · Answer

Oh fancy :-D

sasogeek · Answer

i thought of that ffm but i also thought it'd be too long so i skipped it, i'll try that and let u know what i get

anonymous · Answer

It's not too long, I think you can do that

anonymous · Answer

Lol, not for us Ishaan, saso is a kid :)

anonymous · Answer

Let me rephrase *sweet* kid :D

anonymous · Answer

Maybe you can use something else but it's not a short way either. f(x)=3x+2 is a linear function (Invertible) but I don't recommend it, try to do what FoolForMath told you.

sasogeek · Answer

well i had p=1 and q=$\sqrt{10} $