Question

Functions! Please help, very important! :)
(file attached)

Answer 1

f . g = h

f = 3x + 5
h = 3x^2 + 3x + 2

so f(g(x)) = 3x^2 + 3x + 2

That means:

3(g(x)) + 5 = 3x^2 + 3x + 2

By inspection:

g(x) = x^2 + x - 1

Answer 2

what's inspection, sorry?

Answer 3

Figuring it out by looking at it

Answer 4

I don't follow, how you get this part? 3(g(x)) + 5 = 3x^2 + 3x + 2

Answer 5

we know h(x) = 3x^2 + 3x +2 --------> (1)

and we know f.g = f(g(x))

but f(x) = 3x + 5, therefore f(g(x)) = 3(g(x)) + 5 --------> (2)

and we know that f.g = h ----> f(g(x)) = h(x)

therefore: (1) = (2)

3(g(x)) + 5 = 3x^2 + 3x +2

Answer 6

ohkay, and then you can kinda just look at it and like guess and check and see that x^2+x-1 works for g, right?

Answer 7

Yes. Or you can just solve G like a normal variable:

3(g(x)) + 5 = 3x^2 + 3x +2

Substract 5 on both sides:

3(g(x)) = 3x^2 + 3x -3

Divide by 3:

g(x) = x^2 + x - 1

Answer 8

oh! that's much clearer. thank you so much!

Answer 9

shot

Answer 10

shot?

Answer 11

haha, colloquial for "cool, no problem"