A Combining Functions Question and A Intersect Question

[zuuberbat]

1) Find functions f and g such that F(x) = fog.
a) F(x) = sqrt(9x^2 + 16)
- I don't really understand what the question is asking here... how would I do it?

2) Find the points of intersection of the given functions:
y = -x^2 + 2x + 1
y = x^2 - 6x + 1
- I don't really remember how to find the intersections of functions.

Please help if you can, would appreciate steps and an explanation if possible, thank you.

 

[skeeter]

1) Find functions f and g such that F(x) = fog.
a) F(x) = sqrt(9x^2 + 16)
- I don't really understand what the question is asking here... how would I do it?

\(\displaystyle f \circ g = f[g(x)]\) look at F(x) ... do you see a function inside another function?

2) Find the points of intersection of the given functions:
y = -x^2 + 2x + 1
y = x^2 - 6x + 1
- I don't really remember how to find the intersections of functions.

set them equal to each other and solve for x ...
\(\displaystyle -x^2 + 2x + 1 = x^2 - 6x + 1\)

 

[zuuberbat]

1) For f[g(x)]I know I should replace x in f(x) with g(x), so that it becomes like sqrt(9(g(x))^2 + 16). But I still don't really know what to do.

2) Thanks.
Edit: I figured up to 2x^2 - 8x, but I don't know how to continue on further to find the intersect.

 

[skeeter]

1) For f[g(x)]I know I should replace x in f(x) with g(x), so that it becomes like sqrt(9(g(x))^2 + 16). But I still don't really know what to do.

you don't understand ... the composition has already been done, you just have to recognize it.

look again ...
F(x) = sqrt(9x^2 + 16)

2) Thanks.
Edit: I figured up to 2x^2 - 8x, but I don't know how to continue on further to find the intersect.

2x^2 - 8x equal to what?

 

[zuuberbat]

1) Yeah I really don't recognize what to do.

2) 2x^2 - 8x = 0
2(x^2 - 4x) ? How would I simplify (x^2 - 4x) further?

 

[skeeter]

1) I used the colors for a reason ... g(x) and f(x), help any?

2) try factoring out 2x instead of just 2.

 

[zuuberbat]

1) Oh wow, I knew what fog was, but I was just thinking blindly lol, I understand now thanks.
2) Ah, didn't realize the extra x = =, thanks again.

I understand now, thanks for your time skeeter.