Question

Find f(x) and g(x) so that the function can be described as y = f(g(x)).

Answer 1

f(x)=\[\frac{ 2 }{ x^{2} }\]

Answer 2

@satellite73

Answer 3

Your pick for f(x) won't work because you need the x part to be with g(x). You can choose g(x) = 2/x² though because it's the inside function

Answer 4

Then f(x) is the outside function, so it would be like you substituted 2/x² in for the x in f(x) = x + 9

Answer 5

so f(x)=x+9
f(2/(x^2))=(2/(x^2))+9 is wrong?

Answer 6

that's right because g(x) = 2/x²

Answer 7

so when g(x) = 2/x²,
the x in f(x) = x + 9
f(2/x²)=2/x², +9?

Answer 8

yes that's correct

Answer 9

thank you

Answer 10

so i just write

Answer 11

1) Don't use \(y\) as \(y\) here is actually \(f(g(x))\). So just use \(f(x) \) and \(g(x)\)

2) What you wrote in that last post is not what you wrote before, the latter is incorrect.

You want \(f(x) = x+9\) and \(g(x) = \dfrac{2}{x^2}\).

Now we have \(f(g(x)) = f(\dfrac{2}{x^2})= \dfrac{2}{x^2}+9\) as desired.

Answer 12

I think I misunderstood what you were saying.
f(x) = x + 9
g(x) = 2/x²
The function f(g(x)) = (2/x²) + 9 is a composed function made up of both f(x) and g(x).

Answer 13

so just this:
f(x) and g(x) so that the function can be described as y = f(g(x)).
f(x)= 2/x²+ 9
g(x) = 2/x²

Answer 14

p.s. If you would like to be a smart retriceon the test, there is always one answer that will work.

Let \(g(x) = \frac{2}{x^2}+9\) and let \(f(x) = x\), or vice versa.

This will always work :)

Answer 15

that should say "smart a**"