Question

Given that f(x)=x7+5x+1 and g(x)=7x+8, find [fogof](x) and (f+3g)(-1)

Answer 1

well, why not start calculating

Answer 2

I prefer the other notation, it's a little easier to work with.\[\Large\bf\sf \left[f\circ g\circ f\right](x)\quad=\quad f\left[g(f(x))\right]\]So let's work from the outside first I guess,\[\Large\bf\sf f\left[\color{royalblue}{x}\right]\quad=\quad (\color{royalblue}{x})^7+5(\color{royalblue}{x})+1\]

Answer 3

\[\Large\bf\sf f\left[\color{royalblue}{g(f(x))}\right]\quad=\quad (\color{royalblue}{g(f(x))})^7+5(\color{royalblue}{g(f(x))})+1\]

Answer 4

Hmm ya this is gonna get ugly :O

Answer 5

So I'm plugging f into g here,
\[\Large\bf\sf g(\color{orangered}{x})=7(\color{orangered}{x})+8\qquad\implies\qquad g(\color{orangered}{f(x)})\quad=\quad 7\color{orangered}{f(x)}+8\]Then let's plug f(x) in for the orange part,\[\Large\bf\sf g(\color{orangered}{f(x)})\quad=\quad 7(\color{orangered}{x^7+5x+1})+8\]And now we plug this whole thing in for the blue stuff from earlier.

Answer 6

\[\bf\sf f\left[\color{royalblue}{g(f(x))}\right]\quad=\quad (\color{royalblue}{7(x^7+5x+1)+8})^7+5(\color{royalblue}{7(x^7+5x+1)+8})+1\]

Answer 7

I don't know if the colors are actually helping on this problem.. there are so many layers :(
Kinda gets muddled up and hard to read after a while.

Answer 8

But umm.. you certainly would not want to simplify that... that's for sure :\
Just stop there for the first one... :p

Answer 9

I dunno, you could simplify it a little bit.
But definitely don't expand out the 7th power.
That would be crazy +_+

Answer 10

that's the method zepdrix

Answer 11

What's what method?

Answer 12

the simplification of the above question. thanks

Answer 13

He's got it. Catch you later with a more complicated math equation...

Answer 14

Oh you were just testing us or something? XD lol